Rick Miranda

Publications (Articles)

  1. On the stability of pencils of cubic curves. American Journal of Mathematics, v. 102, no. 6 (1980) 1177-1202.
  2. The moduli of Weierstrass fibrations over P1. Mathematische Annalen, v. 255 (1981) 379-394. PDF File
  3. Smooth models for elliptic threefolds. In: The Birational Geometry of Degenerations, Progress in Mathematics, v. 29, Birkhauser, (1983), 85-133.
  4. The minus one theorem, (with D. Morrison). In: The Birational Geometry of Degenerations, Progress in Mathematics, v. 29, Birkhauser, (1983), 173-259.
  5. Projectively unstable elliptic surfaces. Illinois Journal of Mathematics, v. 27, no. 3, (1983),404-420.
  6. Smoothing cusp singularities of small length, (with R. Friedman). Mathematische Annalen, v. 263 (1983) 185-212.
  7. Integration: why you can and why you can't. Pi Mu Epsilon Journal, v.7, no. 9, (1983), 557-566.
  8. Non-degenerate symmetric bilinear forms on finite abelian 2-groups. Transactions of the AMS, v. 284, no. 2, (1984), 535-542.
  9. Non-classical Godeaux surfaces in characteristic five. Proceedings of the AMS, v.91, no. 1, (1984), 9-11.
  10. Gorenstein toric threefolds with isolated singularities and cyclic divisor class group. Rocky Mountain Journal of Mathematics, v. 15, no. 1, (1985) 39-45.
  11. Triple covers in algebraic geometry. American Journal of Mathematics, v. 107, no. 5 (1985), 1123-1158.
  12. Non-commutative algebras of dimension three over integral schemes, (with M. Teicher). Transactions of the AMS, v. 292, no. 2, (1985), 705-712.
  13. 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.
  14. 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.
  15. On extremal rational elliptic surfaces, (with U. Persson). Mathematische Zeitschrift, v. 193, (1986), 537-558.
  16. On canonical surfaces of general type with $K^2 = 3\chi - 10$. Mathematische Zeitschrift, v. 198, (1988), 83-93
  17. 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.
  18. On the surjectivity of the Wahl map, (with C. Ciliberto and J. Harris). Duke Mathematical Journal, vol. 57, no. 3, (1988), 829-858.
  19. Configurations of $I_n$ fibers on elliptic $K3$ surfaces, (with U. Persson). Mathematische Zeitschrift, v. 201, (1989), 339-361.
  20. 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.
  21. 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).
  22. Galois extensions of prime degree, (with C. Greither). Journal of Algebra, vol. 124, No. 2 (1989), 354-366.
  23. Torsion groups of elliptic surfaces, (with U. Persson). Compositio Mathematica 72 (1989), 249-267.
  24. Exceptional curves on rational numerically elliptic surfaces, (with B. Harbourne). Journal of Algebra, vol. 128, No. 2, (1990), 405-433.
  25. The automorphism groups of the hyperelliptic surfaces, (with C. Bennett). Rocky Mountain Journal of Math., Vol. 26, No. 1, Winter 1990, 31-37.
  26. On the Gaussian map for canonical curves of low genus, (with C. Ciliberto). The Duke Mathematical Journal, vol. 61, No.2 (1990), 417-443.
  27. Persson's list of singular fibers for a rational elliptic surface. Mathematische Zeitschrift vol. 205, (1990), 191-211.
  28. 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.
  29. Instructor's and Student Solutions Manual for: Elementary Linear Algebra (Fourth Edition), by S. Grossman. Saunders College Publishing (1991).
  30. Using RMT: A workbook in Linear Algebra. published by Saunders College Publishing (1991).
  31. RMT: a manual for the PC-compatible version. published by Saunders College Publishing (1991).
  32. 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.
  33. 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.
  34. 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.
  35. Triangulating between parallel splitting contours using a simplicial algorithm, (with C. Fedde and T. McCracken). Proceedings of the Biostereometrics Conference, Boston, MA, 1990.
  36. The Gaussian map for rational ruled surfaces, (with J. Duflot). The Transactions of the AMS, Vol. 330, No. 1, (March 1992), 447-459.
  37. 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.
  38. 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.
  39. 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.
  40. 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. Postscript File
  41. The Cohomological Brauer Group of a Toric Variety, (with F. DeMeyer and T. Ford). Journal of Algebraic Geometry, Vol 2 (1993), 137-154.
  42. 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.
  43. 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.
  44. 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.
  45. The Proto-Lorenz System, (with E. Stone). Physics Letters A, vol. 178 (1993), 105-113. PDF File
  46. Projective Degenerations of K3 Surfaces, Gaussian Maps, and Fano Threefolds, (with A. Lopez and C. Ciliberto). Inventiones mathematicae 114 (1993), 641-667. Postscript File PDF File
  47. Rational singularities and the Brauer Group, (with F. DeMeyer and T. Ford). The Journal of Algebra, Vol. 162, No. 2 (1993), 287-294.
  48. 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.
  49. 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. Postscript File
  50. 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. Postscript File
  51. 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.
  52. 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.
  53. Torsion Sections of Elliptic Surfaces, (with Peter Stiller). Arkiv f\"or Matematik, vol. 33, no. 1 (March 1995) 117-134. Postscript File
  54. 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. PDF File
  55. The Best Least-Squares Line Fit (with D. Alciatore). In: Graphics Gems V, Edited by Alan W. Paeth. Academic Press (1995), 91-97
  56. 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.
  57. 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. Postscript File
  58. Circular Nodes in Neural Networks, (with M. Kirby). Neural Computation, Vol. 8, No. 2 (1996), 390-402. Postscript File
  59. Local to Global Equivalence for Homomorphisms (with Frank DeMeyer and Kim Schneider). Communications in Algebra, Vol. 24(13) (1996), 4225-4237.
  60. 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. Postscript File
  61. 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.
  62. 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. Postscript File
  63. 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.
  64. 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. Postscript File
  65. Degenerations of Planar Linear Systems (with C. Ciliberto). Journal fur die reine und angewandte Mathematik, vol. 501 (1998), 191-220. Postscript File
  66. Numerical Exploitation of Equivariance (with E. Allgower, K. Georg, and J. Tausch Z. Angew. Math. Mech., vol. 78, No. 12 (1998), 795-806. Postscript File
  67. Interpolation on Curvilinear Schemes (with C. Ciliberto). Journal of Algebra, vol. 203 (1998), 677-678. Postscript File
  68. Quadruple Covers in Algebraic Geometry (with David Hahn) Journal of Algebraic Geometry, Vol. 8, (1999), 1-30. Postscript File
  69. Karhunen-Loeve Decomposition in the Presence of Symmetry, I (with Brigitte Lahme) IEEE Transactions on Image Processing, vol. 8, No. 9 (1999), 1183-1190. Postscript File
  70. Linear Systems of Plane Curves Notices of the AMS, Vol. 46, No. 2 (1999), 192-202. Postscript File
  71. 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. Postscript File
  72. 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. Postscript File
  73. Stability of Pencils of Quadrics in $P^4$. (with Dan Avritzer) The Boletin de la Sociedad Matematica Mexicana, (3), vol. 5 (1999), 281-300. Postscript File
  74. 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.
  75. Symmetric Veronese Classifiers with Applications to Materials Design (with M. Kirby and S. Martin) Engineering Applications of Artificial Intelligence, 13 (2000), 513-520.
  76. 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.
  77. Linear Systems of Plane Curves with Base Points of Equal Multiplicity (with C. Ciliberto). Trans. Amer. Math. Soc. 352 (2000), 4037-4050. Postscript File
  78. A Deformation Theory Approach to Linear Systems with General Triple Points (with C. Ciliberto) Le Matematiche, Vol. LV (2000), Fascicolo II, pp. 259--270.
  79. 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
  80. 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. Postscript File
  81. 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. Postscript File
  82. Algebraic Geometry, invited article for The Encyclopedia of Physical Science and Technology, (Academic Press), Third Edition, Volume 1, (2002), 465-475 Postscript File
  83. 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. Postscript File
  84. 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. Postscript File
  85. Topics on Interpolation Problems in Algebraic Geometry (with C. Bocci), Rend. Sem. Mat. Univ. Pol. Torino - Vol. 62, No. 4 (2004), 279-334. Postscript File
  86. Bielliptic Surfaces as Covers of Rational Surfaces. Advances in Mathematics, Vol. 198, Issue 2 (2005), 439-447. Postscript File
  87. 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. Postscript File
  88. Anacapri Lectures on Degenerations of Surfaces, Lecture notes of four lectures at the Anacapri Summer School in Projective Geometry, June 2004. Postscript File
  89. 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. Postscript File
  90. 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. PDF File
  91. 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. PDF File
  92. 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. PDF File
  93. 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. PDF File
  94. Degenerations of the Veronese and Applications (with C. Ciliberto and O. Dumitrescu), Bull. Belg. Math. Soc. Simon Stevin 16(2009), 771-798. PDF File
  95. 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. PDF File
  96. Homogeneous interpolation on ten points (with C. Ciliberto), Journal of Algebraic Geometry 20 (2011) 685-726 PDF File
  97. 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 PDF File
  98. 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 PDF File
  99. The rank of the 2nd Gaussian map for general curves (with A. Calabri and C. Ciliberto), Michigan Mathematics Journal, vol. 60 (2011), 545-559 PDF File
  100. 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. PDF File
  101. Variations on Nagata's Conjecture (with C. Ciliberto, B. Harbourne, and J. Roe') Clay Mathematics Proceedings, Volume 18, 2013, 185--203 PDF File
  102. 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. PDF File
  103. Linear Systems on Edge-Weighted Graphs (with R. James) The Rocky Mountain Journal of Mathematics, Volume 46, Number 5, 2016, 1559--1574 PDF File

Works in Progress

  1. Rick Miranda and David R. Morrison, Embeddings of Integral Quadratic Forms (vii + 221 pages), preliminary draft. PDF File