Algebraic Geometry

Computational Methods

14-04, 14Qxx

  1. Fatima K. Abu Salem and Kamal Khuri-Makdisi, Fast Jacobian group operations for C3,4 curves over a large finite field, LMS J. Comput. Math. 10 (2007), 307–328 (electronic).[MR]
  2. S. Arita, S. Miura, and T. Sekiguchi, An addition algorithm on the Jacobian varieties of curves, J. Ramanujan Math. Soc. 19 (2004), no. 4, 235–251.[MR]
  3. Tobias Beck and Josef Schicho, Adjoint computation for hypersurfaces using formal desingularizations, J. Algebra 320 (2008), no. 11, 3984–3996.[MR/doi]
  4. Tobias Beck and Josef Schicho, Curve parametrization over optimal field extensions exploiting the Newton polygon, Geometric Modeling and Algebraic Geometry, Springer, Berlin, 2008, pp. 119–140.[MR]
  5. Gavin Brown, A database of polarized K3 surfaces, Experiment. Math. 16 (2007), no. 1, 7–20.[MR]
  6. Gavin Brown and Daniel Ryder, Elliptic fibrations on cubic surfaces, J. Pure Appl. Algebra 214 (2010), no. 4, 410–421.[MR/doi]
  7. Gavin Brown and Kaori Suzuki, Computing certain Fano 3-folds, Japan J. Indust. Appl. Math. 24 (2007), no. 3, 241–250.[MR/link]
  8. Laurent Busé and Marc Chardin, Implicitizing rational hypersurfaces using approximation complexes, J. Symbolic Comput. 40 (2005), no. 4-5, 1150–1168.[MR]
  9. Gweltaz Chatel and David Lubicz, A point counting algorithm using cohomology with compact support, preprint (2008), 32 pages.[arXiv]
  10. David A. Cox, John Little, and Donal O'Shea, Using Algebraic Geometry, Graduate Texts in Mathematics, vol. 185, Springer, New York, 2005, pp. xii+572.[MR]
  11. Wolfram Decker and Christoph Lossen, Computing in algebraic geometry, Algorithms and Computation in Mathematics, vol. 16, Springer-Verlag, Berlin, 2006, pp. xvi+327.[MR]
  12. André Galligo and David Rupprecht, Irreducible decomposition of curves, J. Symbolic Comput. 33 (2002), no. 5, 661–677.[MR]
  13. Ralf Gerkmann, Mao Sheng, and Kang Zuo, Computational details on the disproof of modularity, preprint (2007), 16 pages.[arXiv]
  14. Martine Girard and Leopoldo Kulesz, Computation of sets of rational points of genus-3 curves via the Demjanenko-Manin method, LMS J. Comput. Math. 8 (2005), 267–300 (electronic).[MR]
  15. Massimo Giulietti, Algebraic curves over finite fields and MAGMA, Ital. J. Pure Appl. Math. (2000), no. 8, 19–32.[MR]
  16. Willem A. de Graaf, Constructing algebraic groups from their Lie algebras, J. Symbolic Comput. 44 (2009), no. 9, 1223–1233.[arXiv]
  17. Willem A. de Graaf, Michael Harrison, Jana Pílniková, and Josef Schicho, A Lie algebra method for rational parametrization of Severi-Brauer surfaces, J. Algebra 303 (2006), no. 2, 514–529.[MR]
  18. Michael Harrison and Josef Schicho, Rational parametrisation for degree 6 Del Pezzo surfaces using Lie algebras, ISSAC 2006, ACM, New York, 2006, pp. 132–137.[MR]
  19. Hendrik Hubrechts, Memory efficient hyperelliptic curve point counting, preprint (2006), 10 pages.[arXiv]
  20. Gabriela Jeronimo, Teresa Krick, Juan Sabia, and Martín Sombra, The computational complexity of the Chow form, Found. Comput. Math. 4 (2004), no. 1, 41–117.[MR]
  21. Tanja Lange, Formulae for arithmetic on genus 2 hyperelliptic curves, Appl. Algebra Engrg. Comm. Comput. 15 (2005), no. 5, 295–328.[MR]
  22. Alan G. B. Lauder, A recursive method for computing zeta functions of varieties, LMS J. Comput. Math. 9 (2006), 222–269 (electronic).[MR]
  23. Walter D. Neumann and Penelope G. Wightwick, Algorithms for polynomials in two variables, Combinatorial and Computational Algebra (Hong Kong, 1999), Contemp. Math., vol. 264, Amer. Math. Soc., Providence, RI, 2000, pp. 219–235.[MR]
  24. Jana Pílniková, Parametrizing algebraic varieties using Lie algebras, preprint (2006), 74 pages.[arXiv]
  25. Carlos Rito, On equations of double planes with pg = q = 1, Math. Comp 79 (2010), 1091–1108.[arXiv]
  26. Carlos Rito, On the computation of singular plane curves and quartic surfaces, preprint (2010), 13 pages.[arXiv]
  27. Mohab Safey El Din, Testing sign conditions on a multivariate polynomial and applications, Math. Comput. Sci. 1 (2007), no. 1, 177–207.[MR]
  28. Mohab Safey El Din and Éric Schost, Properness defects of projections and computation of at least one point in each connected component of a real algebraic set, Discrete Comput. Geom. 32 (2004), no. 3, 417–430.[MR]
  29. Tanush Shaska, Computational algebra and algebraic curves, Comm. Comp. Alg. 37 (2003), no. 4, 117–124.[link]
  30. Dongming Wang, Decomposing algebraic varieties, Automated Deduction in Geometry (Beijing, 1998), Lecture Notes in Comput. Sci., vol. 1669, Springer, Berlin, 1999, pp. 180–206.[MR]