Rick Miranda
Publications (Articles)
- On the stability of pencils of cubic curves.
American Journal of Mathematics,
v. 102, no. 6 (1980) 1177-1202.
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- The moduli of Weierstrass fibrations over P1.
Mathematische Annalen, v. 255 (1981) 379-394.
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- Smooth models for elliptic threefolds.
In: The Birational Geometry of Degenerations,
Progress in Mathematics, v. 29, Birkhauser, (1983), 85-133.
- The minus one theorem,
(with D. Morrison).
In: The Birational Geometry of Degenerations,
Progress in Mathematics, v. 29, Birkhauser, (1983), 173-259.
- Projectively unstable elliptic surfaces.
Illinois Journal of Mathematics, v. 27, no. 3, (1983),404-420.
- Smoothing cusp singularities of small length,
(with R. Friedman).
Mathematische Annalen, v. 263 (1983) 185-212.
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- Integration: why you can and why you can't.
Pi Mu Epsilon Journal, v.7, no. 9, (1983), 557-566.
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- Non-degenerate symmetric bilinear forms on finite
abelian 2-groups.
Transactions of the AMS, v. 284, no. 2, (1984), 535-542.
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- Non-classical Godeaux surfaces in characteristic
five.
Proceedings of the AMS, v.91, no. 1, (1984), 9-11.
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- Gorenstein toric threefolds with isolated
singularities and cyclic
divisor class group.
Rocky Mountain Journal of Mathematics, v. 15, no. 1,
(1985) 39-45.
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- Triple covers in algebraic geometry.
American Journal of Mathematics, v. 107, no. 5
(1985), 1123-1158.
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- Non-commutative algebras of dimension three
over integral schemes,
(with M. Teicher).
Transactions of the AMS, v. 292, no. 2, (1985), 705-712.
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- The number of embeddings of integral quadratic
forms I,
(with D. Morrison).
Proceedings of the Japan Academy, v. 61, Ser. A, no. 10, (1985), 317-320.
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- The number of embeddings of integral quadratic
forms II,
(with D. Morrison).
Proceedings of the Japan Academy, v. 62, Ser. A,
no. 1, (1986), 29-32.
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- On extremal rational elliptic surfaces,
(with U. Persson).
Mathematische Zeitschrift, v. 193, (1986), 537-558.
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- On canonical surfaces of general type with
$K^2 = 3\chi - 10$.
Mathematische Zeitschrift, v. 198, (1988), 83-93
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- General components of the Noether-Lefschetz
locus and their density in
the space of all surfaces,
(with C. Ciliberto and J. Harris).
Mathematische Annalen, 282,(1988), 667-680.
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- On the surjectivity of the Wahl map,
(with C. Ciliberto and J. Harris).
Duke Mathematical Journal, vol. 57, no. 3, (1988),
829-858.
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- Configurations of $I_n$ fibers on elliptic
$K3$ surfaces,
(with U. Persson).
Mathematische Zeitschrift, v. 201, (1989), 339-361.
- Galois cubic extensions of commutative rings.
Section 3 of: "Quadratic Forms over $\Bbb Q$ and
Galois extension of
commutative rings", by F. DeMeyer, D. Harrison,
and R. Miranda.
Memoirs of the AMS, vol. 77, number 394, (1989), 43-63.
- Six lectures on graph curves and curves on
K3 surfaces.
In: Lectures on Riemann surfaces, Proceedings of
the College on Riemann
surfaces, International Centre for Theoretical
Physics, Trieste,
Italy, 9 Nov. - 18 Dec. 1987; pp. 119 - 176.
World Scientific
(1989).
- Galois extensions of prime degree,
(with C. Greither).
Journal of Algebra, vol. 124, No. 2 (1989), 354-366.
- Torsion groups of elliptic surfaces,
(with U. Persson).
Compositio Mathematica 72 (1989), 249-267.
- Exceptional curves on rational numerically
elliptic surfaces,
(with B. Harbourne).
Journal of Algebra, vol. 128, No. 2, (1990), 405-433.
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- The automorphism groups of the hyperelliptic
surfaces,
(with C. Bennett).
Rocky Mountain Journal of Math., Vol. 26, No. 1, Winter 1990, 31-37.
- On the Gaussian map for canonical curves
of low genus,
(with C. Ciliberto).
The Duke Mathematical Journal, vol. 61, No.2
(1990), 417-443.
- Persson's list of singular fibers for a
rational elliptic surface.
Mathematische Zeitschrift vol. 205, (1990), 191-211.
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- The Gaussian map for certain planar graph
curves.
In: Algebraic Geometry: Sundance 1988. B.
Harbourne and R. Speiser, editors. Contemporary Mathematics 116 (1991), 115-124.
- Instructor's and Student Solutions Manual
for: Elementary Linear Algebra (Fourth Edition), by S. Grossman.
Saunders College Publishing (1991).
- Using RMT: A workbook in Linear Algebra.
published by Saunders College Publishing (1991).
- RMT: a manual for the PC-compatible version.
published by Saunders College Publishing (1991).
- The Mordell-Weil groups of extremal elliptic
K3 surfaces,
(with Ulf Persson).
In: Problems in the Theory of Surfaces and their Classification,
Symposia Mathematica XXXII, F. Catanese, C. Ciliberto, M.
Cornalba, editors. Academic Press (1991), 167-192.
- Some thoughts on a computer workstation
for the biological sciences,
(with T.O. McCracken, T.L. Spurgeon, L.G. Lodise, S.K. Koch,
and C. Fedde).
In: ``Workstations for Experiments'',
Jos\'e L. Encarnacao and Georges G. Grinstein, Editors.
IFIP Series on Computer Graphics, IFIP WG 5.10,
Proceedings of International Working Conference, Lowell, MA,
USA, July 1989.
Springer-Verlag (1991), 161-163.
- Gaussian maps for certain families of canonical
curves,
(with C. Ciliberto).
In: Complex Projective Geometry,
edited by G. Ellingsrud, C. Peskine, G. Sacchiero, and S.A.
Stromme.
London Mathematical Society Lecture Note Series No. 179,
Cambridge University Press (1992), 106-127.
- Triangulating between parallel splitting
contours using a simplicial algorithm,
(with C. Fedde and T. McCracken).
Proceedings of the Biostereometrics Conference,
Boston, MA, 1990.
- The Gaussian map for rational ruled surfaces,
(with J. Duflot).
The Transactions of the AMS, Vol. 330, No. 1, (March 1992), 447-459.
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- Exploiting symmetry in solving linear equations,
(with K. Georg).
In: Bifurcation and Symmetry,
edited by E. Allgower, K. B\"ohmer, and M. Golubitsky.
International Series of Numerical Mathematics, Vol. 104,
Birkh\"auser Verlag Basel (1992), 157-168.
- The Method of Resultants for Computing Real
Solutions of Polynomial Systems,
(with E. Allgower and K. Georg).
Siam Journal of Numerical Analysis, Vol. 20, No. 3
(June 1992), 831-844.
- Exploiting Symmetry in Boundary Element Methods,
(With E. Allgower, K. B\"ohmer, and K. Georg).
SIAM Journal of Numerical Analysis, vol. 29 (1992), 534-552.
- Colorings of Planar Maps and Residues of $1$-forms.
In: Methods in Module Theory,
G. Abrams, J. Haefner, and K.M. Rangaswamy, eds.
Lecture Notes in Pure and Applies Mathematics,
Marcel Dekker, Vol. 140, (1993), 237-248.
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- The Cohomological Brauer Group of a Toric Variety,
(with F. DeMeyer and T. Ford).
Journal of Algebraic Geometry, Vol 2 (1993), 137-154.
- Building Three-dimensional Computer Graphics
Surface Models
for Anatomy Education,
(with D. Alciatore).
Proc. of the 1992 ASME International Computers in
Engineering Conference,
San Francisco, CA, August 1992.
- Exploiting Permutation Symmetry with Fixed Points
in Linear Equations,
(with Eugene Allgower and Kurt Georg)
in: Exploiting Symmetry in Applied and Numerical Analysis,
E. L. Allgower, K. Georg, and R. Miranda, Eds.
AMS Lectures in Applied Mathematics, Volume 29 (1993), 23-36.
- Symmetry aspects in numerical linear algebra with
applications to
boundary element methods,
(with K. Georg).
in: Exploiting Symmetry in Applied and Numerical Analysis,
E. L. Allgower, K. Georg, and R. Miranda, Eds.
AMS Lectures in Applied Mathematics, Volume 29 (1993), 213-228.
- The Proto-Lorenz System,
(with E. Stone).
Physics Letters A, vol. 178 (1993), 105-113.
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- Projective Degenerations of K3 Surfaces, Gaussian Maps,
and Fano Threefolds,
(with A. Lopez and C. Ciliberto).
Inventiones mathematicae 114 (1993), 641-667.
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- Rational singularities and the Brauer Group,
(with F. DeMeyer and T. Ford).
The Journal of Algebra, Vol. 162, No. 2 (1993), 287-294.
- The Nonlinear Reduction of High-Dimensional
Dynamical Systems
via Neural Networks,
(with Michael Kirby).
Physical Review Letters, Volume 72, Number 12
(21 March 1994), 1822-1825.
- Component Numbers for Torsion Sections
of Semistable Elliptic Surfaces.
In:Classification of Algebraic Varieties,
C. Ciliberto, E. L. Livorni, and A. J. Sommese, editors.
AMS Contemporary Mathematics, Volume 162 (1994), 293-311.
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- Graph Curves, Colorings, and Matroids,
(with C. Ciliberto).
In: Zero-Dimensional Schemes. Proceedings of the
International Conference held in Ravello, Italy, June 1992;
F. Orecchia and L. Chiantini,
Eds. Walter de Gruyter, Berlin, New York (1994), 89-111.
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- The Remodeling of Chaotic Dynamical Systems,
(with M. Kirby).
In: Intelligent Engineering Systems Through Artificial Neural Networks,
Vol. 4, C. H. Dagli, B. R. Fernandez, J. Ghosh, and R. T. S. Kumara, Eds.
Proceedings of the ANNIE '94 conference, St. Louis, MO,
ASME Press, New York, 831-836.
- Elliptic Surfaces and the Mordell-Weil Group.
Matem\'atica Contempor\^anea, Vol. 6, (1994), 147-195.
``XII Escola de Algebra'', August 1992, Diamantina,
Minas Gerais, Brazil.
- Torsion Sections of Elliptic Surfaces,
(with Peter Stiller).
Arkiv f\"or Matematik, vol. 33, no. 1 (March 1995) 117-134.
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- Quantum Cohomology of Rational Surfaces,
(with B. Crauder).
In: The Moduli Space of Curves,
Edited by R. Dijkgraaf, C. Faber, and G. van der Geer.
Birhauser Press, Boston (1995), 35-82.
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- The Best Least-Squares Line Fit
(with D. Alciatore).
In: Graphics Gems V, Edited by Alan W. Paeth.
Academic Press (1995), 91-97
- Spherical Nodes in Neural Networks
(with D. Hundley and M. Kirby).
In: Intelligent Engineering Systems through Artificial Neural Networks,
C.H. Dagli et al, Editors. 1995 ASME Press.
- On the Corank of Gaussian Maps for General
Embedded $K3$ Surfaces,
(with A. Lopez and C. Ciliberto).
In: Proceedings of the Hirzebruch $65$
Conference on Algebraic Geometry, May 2-7, 1993,
Mina Teicher, editor.
Israel Mathematical Conference Proceedings, Volume 9 (1996), 141-157.
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- Circular Nodes in Neural Networks,
(with M. Kirby).
Neural Computation, Vol. 8, No. 2 (1996), 390-402.
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- Local to Global Equivalence for Homomorphisms
(with Frank DeMeyer and Kim Schneider).
Communications in Algebra, Vol. 24(13) (1996), 4225-4237.
- Some Remarks on the Obstructedness of Cones
over Curves of Low Genus
(with A. Lopez and C. Ciliberto).
In: ``Higher Dimensional Complex Varieties'',
Proceedings of the International Conference held in Trento, Italy,
June 15-24, 1994; M. Andreatta and T. Peternell, editors.
Walter de Gruyter, Berlin, New York, (1996), 167-182.
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- Gallery
(with T. McCracken, T. Spurgeon, D. Alciatore, C. Fedde, D. Steward, P. Guzy,
F. Forney, and M. Foerster)
Journal of Biocommunication, Vol. 23, No. 1 (1996) 18-21.
- An Overview of Algebraic Surfaces
In: Algebraic Geometry, edited by Sinan Sertoz.
Lecture note in Pure and Applied Mathematics, Vol. 193,
Marcel Dekker (1997), 157-218.
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- Examples of the Failure of the Local to Global Principle
for Similarity of Matrices
(with Frank DeMeyer and Kim Schneider)
Communications in Algebra, Vol 26, No. 12 (1998), 4179-4185.
- On the Classification of Varieties with Canonical
Curve Section,
(with A. Lopez and C. Ciliberto).
The American Journal of Mathematics, Vol. 120 (1998), 1-21.
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- Degenerations of Planar Linear Systems
(with C. Ciliberto).
Journal fur die reine und angewandte Mathematik, vol. 501 (1998), 191-220.
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- Numerical Exploitation of Equivariance
(with E. Allgower, K. Georg, and J. Tausch
Z. Angew. Math. Mech., vol. 78, No. 12 (1998), 795-806.
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- Interpolation on Curvilinear Schemes
(with C. Ciliberto).
Journal of Algebra, vol. 203 (1998), 677-678.
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- Quadruple Covers in Algebraic Geometry
(with David Hahn)
Journal of Algebraic Geometry, Vol. 8, (1999), 1-30.
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- Karhunen-Loeve Decomposition in the Presence of Symmetry, I
(with Brigitte Lahme)
IEEE Transactions on Image Processing, vol. 8, No. 9 (1999), 1183-1190.
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- Linear Systems of Plane Curves
Notices of the AMS, Vol. 46, No. 2 (1999), 192-202.
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- Empirical Dynamical Systems Reduction I:
Global Nonlinear Transformations
(with M. Kirby)
Semi-Analytic Methods for the Navier-Stokes Equations
(Montreal, 1995) (K. Coughlin, ed.) CRM Proc. Lecture Notes, vol. 20,
Amer. Math. Soc., Providence, RI, 1999, pp. 41-64.
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- Empirical Dynamical Systems Reduction II: Neural Charts
(with D. Hundley and M. Kirby)
Semi-Analytic Methods for the Navier-Stokes
Equations (Montreal, 1995) (K. Coughlin, ed.) CRM Proc. Lecture Notes, vol. 20,
Amer. Math. Soc., Providence, RI, 1999, pp. 65-83.
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- Stability of Pencils of Quadrics in $P^4$.
(with Dan Avritzer)
The Boletin de la Sociedad Matematica Mexicana, (3), vol. 5 (1999), 281-300.
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- On the Wahl Map of Plane Nodal Curves
(with Ciro Ciliberto and Angelo Lopez)
In: Complex Analysis and Algebraic Geometry,
a volume in Memory of Michael Schneider.
Thomas Peternell and Frank-Olaf Schreyer, editors.
Walter de Gruyter, Berlin/New York 2000. 155-163.
- Symmetric Veronese Classifiers with Applications to
Materials Design
(with M. Kirby and S. Martin)
Engineering Applications of Artificial Intelligence, 13 (2000), 513-520.
- Kernel/Feature Selection for Support Vector Machines
Applied to Materials Design}
(with M. Kirby and S. Martin)
In: Proceedings of the IFAC Symposium on Artificial Intelligence
in Real Time Control
(AIRTC-2000), Budapest, Hungary, pp. 29-34. Elsevier Science 2000.
- Linear Systems of Plane Curves with Base Points of Equal Multiplicity
(with C. Ciliberto).
Trans. Amer. Math. Soc. 352 (2000), 4037-4050.
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- A Deformation Theory Approach to Linear Systems
with General Triple Points
(with C. Ciliberto)
Le Matematiche, Vol. LV (2000), Fascicolo II, pp. 259--270.
- Explicit Resolutions of Double Point Singularities of Surfaces
(with A. Calabri and R. Ferraro).
withdrawn, new version by Calabri and Ferraro submitted.
AG E-Prints URL
- Pillow Degenerations of K3 Surfaces
(with C. Ciliberto and M. Teicher)
In: Applications of Algebraic Geometry to Coding Theory,
Physics and Computation,
NATO Science Series II (Mathematics, Physics and Chemistry),
Volume 36 (2001), 53-64.
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- The Segre and Harbourne-Hirschowitz Conjectures
(with C. Ciliberto)
In: Applications of Algebraic Geometry to Coding Theory,
Physics and Computation.
NATO Science Series II (Mathematics, Physics and Chemistry),
Volume 36 (2001), 37--52.
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- Algebraic Geometry,
invited article for
The Encyclopedia of Physical Science and Technology,
(Academic Press), Third Edition, Volume 1, (2002), 465-475
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- Bivariate Hermite Interpolation and Linear Systems of Plane
Curves with Base Fat Points
(with C. Ciliberto, F. Cioffi, and F. Orrechia),
the Proceedings of the Asian Symposium on Computer Mathematics 2003,
87-102.
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- On the Geometric Genus of Reducible Surfaces and
Degenerations of Surfaces to Unions of Planes,
(with A. Calabri, C. Ciliberto, F. Flamini),
The Proceedings of the Fano Conference,
Edited by A. Collino, A. Conte, and M. Marchisio.
Universita' degli Studi di Torino, (2004), 277-312.
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- Topics on Interpolation Problems in Algebraic Geometry
(with C. Bocci),
Rend. Sem. Mat. Univ. Pol. Torino - Vol. 62, No. 4 (2004), 279-334.
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- Bielliptic Surfaces as Covers of Rational Surfaces.
Advances in Mathematics, Vol. 198, Issue 2 (2005), 439-447.
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- Matching Conditions for Degenerating Plane Curves and Applications,
(with C. Ciliberto),
In: Projective Varieties with Unexpected Properties:
a volume in Memory of Giuseppe Veronese;
proceedings of the international conference 'Varieties with Unexpected Properties',
Siena, Italy, June 8-13, 2004.
Editors: C. Ciliberto, A. V. Geramita, B. Harbourne, R. M. Miro-Roig, and K. Ranestad.
Walter de Gruyter (2005), 177--197.
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- Anacapri Lectures on Degenerations of Surfaces,
Lecture notes of four lectures at the Anacapri Summer School in
Projective Geometry, June 2004.
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- Nagata s conjecture for a square or nearly-square number of points,
(with C. Ciliberto);
Ricerche di matematica, Volume 55, Number 1, July 2006, 71 -- 78.
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- Degenerations of Scrolls to Unions of Planes,
(with A. Calabri, C. Ciliberto, and F. Flamini),
Atti Accad. Naz. Lincei Cl. Sci.
Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 17 (2006), no. 2, 95--123.
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- On the K^2 of degenerations of surfaces
and the multiple point formula,
(with A. Calabri, C. Ciliberto, F. Flamini),
Annals of Mathematics, Vol. 165 (2007), 335-395.
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- Non-special scrolls with general moduli
(with A. Calabri, C. Ciliberto, and F. Flamini),
Rendiconti del Circolo Matematico di Palermo, Vol. 57, No. 1 (April 2008), 1-31.
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- Braid monodromy factorization for a non-prime K3 surface branch curve,
(with M. Amram, C. Ciliberto, and M. Teicher),
Israel Journal of Mathematics, Volume 170, Number 1 (2009), 61-93.
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- Degenerations of the Veronese and Applications
(with C. Ciliberto and O. Dumitrescu),
Bull. Belg. Math. Soc. Simon Stevin 16(2009), 771-798.
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- Brill-Noether theory and non-special scrolls
(with A. Calabri, C. Ciliberto, and F. Flamini),
Geometriae Dedicata, vol. 139, no. 1 (April 2009), 121-138.
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- Homogeneous interpolation on ten points
(with C. Ciliberto),
Journal of Algebraic Geometry 20 (2011) 685-726
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- Special Scrolls whose base curve has general moduli
(with A. Calabri, C. Ciliberto, and F. Flamini),
Interactions of Classical and Numerical Algebraic Geometry, 133-155.
Contemporary Math., 496, Americican Mathematics Society, Providence, RI 2009
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- Emptiness of homogeneous linear systems with ten general base points
(with C. Ciliberto, O. Dumitrescu, and J. Roe'),
Classification of algebraic varieties, 189-195.
EMDS Ser. Congr. Rep., Eur. Math. Soc., Zurich 2011
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- The rank of the 2nd Gaussian map for general curves
(with A. Calabri and C. Ciliberto),
Michigan Mathematics Journal, vol. 60 (2011), 545-559
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- Recent developments and open problems in linear series
(with Thomas Bauer, Cristiano Bocci, Susan Cooper, Sandra Di Rocco,
Martin Dumnicki, Brian Harbourne,
Kelly Jabbusch, Andreas L. Knutsen, Alex Kuronya, Joaquim Roe',
Hal Schenck, Tomasz Szemberg,
and Zach Teitler),
In: Contributions to Algebraic Geometry - Impanga Lecture Notes.
Piotr Pragacz, editor. European Mathematical Society (2012), 93--140.
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- Variations on Nagata's Conjecture
(with C. Ciliberto, B. Harbourne, and J. Roe')
Clay Mathematics Proceedings, Volume 18, 2013, 185--203
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- A Riemann-Roch Theorem for edge-weighted graphs
(with R. James),
The Proceedings of the American Mathematical Society, Vol.141, No. 11 (November 2013), 3793-3802.
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- A Riemann-Roch Theory on finite sets
(with R. James),
Journal of Singularities, Volume 9, 2014, 75-81.
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- Linear Systems on Edge-Weighted Graphs
(with R. James)
The Rocky Mountain Journal of Mathematics, Volume 46, Number 5, 2016, 1559--1574
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- Corrigendum to the paper “On the K^2 of degenerations of surfaces and the multiple point formula"
(with Calabri, A. and Ciliberto, C. and Flamini, F.)
Annals of Mathematics, Second Series, Volume 186 (2017), 315-318
Link to Journal
- A few questions about curves on surfaces
(with Ciliberto, Ciro; Knutsen, Andreas Leopold; Lesieutre, John; Lozovanu, Victor; Mustopa, Yusuf; and Testa, Damiano)
Rendiconti del Circolo Matematico di Palermo. Second Series, Volume 66, No. 2 (2017) 195-204
Link to Journal
- Corrigendum to “Classification of varieties with canonical curve section via Gaussian maps on canonical curves”
(with Ciliberto, C. and Lopez, A.)
American J of Math, Volume 143, No. 6 (2021), 1661-1663
- The moduli space of rational elliptic surfaces of index two
(with A. Zanardini)
Link to Journal
Indagationes Mathematicae
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- Examples of non-effective rays at the boundary of the Mori cone of blow-ups of the plane
(with C. Ciliberto).
Rend. Istit. Mat. Univ. Trieste, Vol. 54 (2022), Art. No. 4, 9 pages.
DOI: 10.13137/2464-8728/33880
Link to Journal
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- Dumitrescu, O., Miranda, R. Cremona Orbits in P^4 and Applications.
In: Dedieu, T., Flamini, F., Fontanari, C., Galati, C., Pardini, R. (eds) The Art of Doing Algebraic Geometry. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-11938-5_7, (2023) pp 161--185.
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- C. Ciliberto, R. Miranda: Non-effective planar linear systems at the boundary of the Mori cone
(2022), To appear
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- Dumitrescu, O., Miranda, R.: On (i)-curves in blowups of P^r.
Submitted; arXiv:2104.14141 [math.AG]
- Dumitrescu, O., Miranda, R.: Coxeter theory for curves on blowups of P^r
Submitted; arXiv:2205.13605 [math.AG]
- C. Ciliberto, J. Roe', R. Miranda: Irrational NEF Rays at the Boundary of the Mori Cone for very General Blowups of the Plane
To appear in the Michigan Mathematical Journal
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Works in Progress
- Rick Miranda and David R. Morrison, Embeddings of Integral Quadratic Forms (vii + 221 pages), preliminary draft.
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