Algebraic Geometry

Surfaces and Higher Dimensional Varieties

14Jxx

  1. Selma Altınok, Gavin Brown, and Miles Reid, Fano 3-folds, K3 surfaces and graded rings, Topology and Geometry: Commemorating SISTAG, Contemp. Math., vol. 314, Amer. Math. Soc., Providence, RI, 2002, pp. 25–53.[MR]
  2. Arthur Baragar and Ronald van Luijk, K3 surfaces with Picard number three and canonical vector heights, Math. Comp. 76 (2007), no. 259, 1493–1498 (electronic).[MR]
  3. I. C. Bauer, F. Catanese, and F. Grunewald, The classification of surfaces with pg = q = 0 isogenous to a product of curves, Pure Appl. Math. Q. 4 (2008), no. 2, part 1, 547–586.[MR/arXiv]
  4. Ingrid C. Bauer and Fabrizio Catanese, A volume maximizing canonical surface in 3-space, Comment. Math. Helv. 83 (2008), no. 2, 387–406.[MR]
  5. Ingrid Bauer, Fabrizio Catanese, and Fritz Grunewald, Beauville surfaces without real structures, Geometric Methods in Algebra and Number Theory, Progr. Math., vol. 235, Birkhäuser Boston, Boston, MA, 2005, pp. 1–42.[MR]
  6. Ingrid Bauer, Fabrizio Catanese, and Fritz Grunewald, The absolute Galois group acts faithfully on the connected components of the moduli space of surfaces of general type, preprint (2007), 13 pages.[arXiv]
  7. Ingrid Bauer, Fabrizio Catanese, Fritz Grunewald, and Roberto Pignatelli, Quotients of a product of curves by a finite group and their fundamental groups, preprint (2008), 37 pages.[arXiv]
  8. Ingrid C. Bauer, Fabrizio Catanese, and Roberto Pignatelli, Complex surfaces of general type: Some recent progress, Global Aspects of Complex Geometry, Springer, Berlin, 2006, pp. 1–58.[MR]
  9. Ingrid C. Bauer, Fabrizio Catanese, and Roberto Pignatelli, The moduli space of surfaces with K2 = 6 and pg = 4, Math. Ann. 336 (2006), no. 2, 421–438.[MR]
  10. Ingrid Bauer, Fabrizio Catanese, and Roberto Pignatelli, Surfaces of general type with geometric genus zero: A survey, preprint (2010), 41 pages.[arXiv]
  11. Ingrid Bauer and Roberto Pignatelli, The classification of minimal product-quotient surfaces with pg = 0, preprint (2010), 53 pages.[arXiv]
  12. Tobias Beck, Formal desingularization of surfaces: the Jung method revisited, J. Symb. Comput. 44 (2009), no. 2, 131–160.[doi/arXiv]
  13. Tobias Beck and Josef Schicho, Adjoint computation for hypersurfaces using formal desingularizations, J. Algebra 320 (2008), no. 11, 3984–3996.[MR/doi]
  14. Gilberto Bini, Quotients of hypersurfaces in weighted projective space, preprint (2009), 13 pages.[arXiv]
  15. Hans-Christian Graf v. Bothmer, Finite field experiments, Higher-dimensional Geometry over Finite Fields, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., vol. 16, IOS, Amsterdam, 2008, pp. 1–62.[MR]
  16. Martin Bright, Brauer groups of diagonal quartic surfaces, J. Symbolic Comput. 41 (2006), no. 5, 544–558.[MR]
  17. S. Allen Broughton, Enumeration of the equisymmetric strata of the moduli space of surfaces of low genus, Preprint, 25 pages.
  18. Gavin Brown, Datagraphs in algebraic geometry and K3 surfaces, Symbolic and Numerical Scientific Computation (Hagenberg, 2001), Lecture Notes in Comput. Sci., vol. 2630, Springer, Berlin, 2003, pp. 210–224.[MR]
  19. Gavin Brown, Graded rings and special K3 surfaces, Discovering Mathematics with Magma, Algorithms Comput. Math., vol. 19, Springer, Berlin, 2006, pp. 137–159.[MR]
  20. Gavin Brown, A database of polarized K3 surfaces, Experiment. Math. 16 (2007), no. 1, 7–20.[MR]
  21. Gavin Brown, Alexander Kasprzyk, and Daniel Ryder, Computational birational geometry of minimal rational surfaces, preprint (2009), 20 pages.[arXiv]
  22. Gavin Brown and Kaori Suzuki, Computing certain Fano 3-folds, Japan J. Indust. Appl. Math. 24 (2007), no. 3, 241–250.[MR/link]
  23. Gavin Brown and Kaori Suzuki, Fano 3-folds with divisible anticanonical class, Manuscripta Math. 123 (2007), no. 1, 37–51.[MR/doi]
  24. Nils Bruin, Visualising Sha[2] in abelian surfaces, Math. Comp. 73 (2004), no. 247, 1459–1476 (electronic).[MR]
  25. Anita Buckley and Balázs Szendröi, Orbifold Riemann-Roch for threefolds with an application to Calabi-Yau geometry, J. Algebraic Geom. 14 (2005), no. 4, 601–622.[MR]
  26. Jorge Caravantes, Low codimension Fano–Enriques threefolds, preprint (2006), 27 pages.[arXiv]
  27. A. Clingher, C. F. Doran, J. Lewis, and U. Whitcher, Normal forms, K3 surface moduli, and modular parametrizations, in Groups and Symmetries: Proceedings of the CRM conference in honor of John McKay,, CRM-AMS Proceedings and Lecture Notes, vol. 47, 2008, 18 pages.
  28. Patrick Corn, Tate-Shafarevich groups and K3 surfaces, Math. Comp., to appear (2007), 17 pages.
  29. Alessio Corti and Miles Reid, Weighted Grassmannians, Algebraic Geometry, de Gruyter, Berlin, 2002, pp. 141–163.[MR]
  30. Ulrich Derenthal, On the Cox ring of del Pezzo surfaces, preprint (2006), 17 pages.[arXiv]
  31. Ulrich Derenthal, Universal torsors of del Pezzo surfaces and homogeneous spaces, Adv. Math. 213 (2007), no. 2, 849–864.[MR]
  32. Luis V. Dieulefait, Computing the level of a modular rigid Calabi-Yau threefold, Exp. Math 13 (2004), no. 2, 165-169.
  33. Noam D. Elkies, Three lectures on elliptic surfaces and curves of high rank, preprint (2007), 14 pages.[arXiv]
  34. Pavel Etingof, Alexei Oblomkov, and Eric Rains, Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces, Adv. Math. 212 (2007), no. 2, 749–796.[MR]
  35. Alice Garbagnati and Alessandra Sarti, Elliptic fibrations and symplectic automorphisms on K3 surfaces, Comm. Algebra 37 (2009), no. 10, 3601–3631.[MR/doi]
  36. Shelly Garion and Matteo Penegini, New Beauville surfaces, moduli spaces and finite groups, preprint (2009), 36 pages.[arXiv]
  37. Victor Ginzburg, Calabi-Yau algebras, preprint (2007), 79 pages.[arXiv]
  38. 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]
  39. Willem A. de Graaf, Jana Pílniková, and Josef Schicho, Parametrizing del Pezzo surfaces of degree 8 using Lie algebras, J. Symbolic Comput. 44 (2009), no. 1, 1–14.[arXiv]
  40. V. A. Gritsenko, K. Hulek, and G. K. Sankaran, The Kodaira dimension of the moduli of K3 surfaces, Invent. Math. 169 (2007), no. 3, 519–567.[MR]
  41. Johan P. Hansen, Toric surfaces and codes, techniques and examples, Preprint Series No.1., University of Aarhus, Department of Mathematics, Aarhus, Denmark (2004), 12 pages.
  42. Brendan Hassett, Anthony Vàrilly-Alvarado, and Patrick Varilly, Transcendental obstructions to weak approximation on general K3 surfaces, preprint (2010), 24 pages.[arXiv]
  43. Kiran S. Kedlaya, Computing zeta functions of surfaces, Mathematisches Forschungsinstitut Oberwolfach Report 32 (2005), 1808–1810.
  44. Adam Logan, The Brauer-Manin obstruction on del Pezzo surfaces of degree 2 branched along a plane section of a Kummer surface, Math. Proc. Cambridge Philos. Soc. 144 (2008), no. 3, 603–622.[MR]
  45. Ronald van Luijk, Quartic K3 surfaces without nontrivial automorphisms, Math. Res. Lett. 13 (2006), no. 2-3, 423–439.[MR/arXiv]
  46. Ronald van Luijk, K3 surfaces with Picard number one and infinitely many rational points, Algebra and Number Theory 1 (2007), no. 1, 1–15.
  47. Ronald van Luijk, An elliptic K3 surface associated to Heron triangles, J. Number Theory 123 (2007), no. 1, 92–119.[MR]
  48. Stefan Maubach and Roel Willems, Polynomial automorphisms over finite fields: Mimicking non-tame and tame maps by the Derksen group, preprint (2009), 22 pages.[arXiv]
  49. Jan-Steffen Müller, Explicit Kummer surface theory for arbitrary characteristic, London Math. Soc. J. Comput. Math. 13 (2010), 47–64.[arXiv]
  50. Francesco Polizzi, Standard isotrivial fibrations with pg = q = 1, Journal of Algebra 321 (2009), no. 6, 1600–1631.[doi/arXiv]
  51. Gopal Prasad and Sai-Kee Yeung, Fake projective planes, Invent. Math. 168 (2007), no. 2, 321–370.[MR]
  52. Carlos Rito, On surfaces with pg = q = 1 and non-ruled bicanonial involution, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 6 (2007), no. 1, 81–102.[MR/arXiv]
  53. Carlos Rito, A note on Todorov surfaces, Osaka J. Math. 46 (2009), no. 3, 685–693.[MR/link]
  54. Carlos Rito, Involutions on surfaces with pg = q = 1, Collectanea Mathematica 61 (2010), no. 1, 81–106.[arXiv]
  55. Carlos Rito, On equations of double planes with pg = q = 1, Math. Comp 79 (2010), 1091–1108.[arXiv]
  56. Maria Marti Sanchez, Even sets of (-4)-curves on rational surface, preprint (2010), 17 pages.[arXiv]
  57. Stefan Schröer, Kummer surfaces for the self-product of the cuspidal rational curve, J. Algebraic Geom. 16 (2007), no. 2, 305–346.[MR/arXiv]
  58. Matthias Schütt, Tetsuji Shioda, and Ronald van Luijk, Lines on Fermat surfaces, J. Number Theory 130 (2010), no. 9, 1939–1963.[doi]
  59. James P Smith, Picard-Fuchs differential equations for families of K3 surfaces, PhD Thesis, University of Warwick, 2007.[arXiv]
  60. Kaori Suzuki, On Fano indices of Q-Fano 3-folds, Manuscripta Math. 114 (2004), no. 2, 229–246.[MR]
  61. Damiano Testa, Anthony Vàrilly-Alvarado, and Mauricio Velasco, Cox rings of degree one del Pezzo surfaces, Algebra and Number Theory 3 (2009), 729–761.[arXiv]
  62. Anthony Várilly-Alvarado, Weak approximation on del Pezzo surfaces of degree 1, Adv. Math. 219 (2008), no. 6, 2123–2145.[MR]
  63. Anthony Vàrilly-Alvarado and Bianca Viray, Failure of the Hasse principle for Enriques surfaces, Advances in Mathematics 226 (2011), 4884–4901.[arXiv]
  64. Anthony Várilly-Alvarado and David Zywina, Arithmetic E8 lattices with maximal Galois action, LMS J. Comput. Math. 12 (2009), 144–165.[MR/arXiv]
  65. Bogdan G. Vioreanu, Mordell-Weil problem for cubic surfaces, numerical evidence, preprint (2008), 22 pages.[arXiv]
  66. Bianca Viray, A family of varieties with exactly one pointless rational fiber, preprint (2009), 4 pages.[arXiv]