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.
  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.
  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.
  46. Projective Degenerations of K3 Surfaces, Gaussian Maps, and Fano Threefolds, (with A. Lopez and C. Ciliberto). Inventiones mathematicae 114 (1993), 641-667.
  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.
  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.
  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.
  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.
  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. 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.
  57. Circular Nodes in Neural Networks, (with M. Kirby). Neural Computation, Vol. 8, No. 2 (1996), 390-402.
  58. Local to Global Equivalence for Homomorphisms (with Frank DeMeyer and Kim Schneider). Communications in Algebra, Vol. 24(13) (1996), 4225-4237.
  59. On the Classification of Varieties with Canonical Curve Section, (with A. Lopez and C. Ciliberto). to appear in the Americal Journal of Mathematics.
  60. Some Remarks on the Obstructedness of Cones over Curves of Low Genus (with A. Lopez and C. Ciliberto). to appear.
  61. Spherical Nodes in Neural Networks (with D. Hundley and M. Kirby). submitted.
  62. An Overview of Algebraic Surfaces Five lectures given at the Summer School in Algebraic Geometry, Bilkent University, Ankara, Turkey, August 7-19, 1995. 40 pages, to appear.