publication . Other literature type . Preprint . Article . 2006

On normal K3 surfaces

Ichiro Shimada;
Open Access English
  • Published: 19 Jul 2006
  • Publisher: University of Michigan, Department of Mathematics
We determine all possible configurations of rational double points on complex normal algebraic K3 surfaces, and on normal supersingular K3 surfaces in characteristic p > 19.
free text keywords: 14J28, Mathematics - Algebraic Geometry, General Mathematics, 410, Algebraic number, Pure mathematics, Mathematics, Algebra
25 references, page 1 of 2

[1] M. Artin. Some numerical criteria for contractability of curves on algebraic surfaces. Amer. J. Math., 84:485-496, 1962. [OpenAIRE]

[2] M. Artin. On isolated rational singularities of surfaces. Amer. J. Math., 88:129-136, 1966.

[3] M. Artin. Supersingular K3 surfaces. Ann. Sci. E´cole Norm. Sup. (4), 7:543-567 (1975), 1974.

[4] W. P. Barth, K. Hulek, C. A. M. Peters, and A. Van de Ven. Compact complex surfaces. Springer-Verlag, Berlin, second edition, 2004.

[5] J. W. S. Cassels. Rational quadratic forms. Academic Press Inc. [Harcourt Brace Jovanovich Publishers], London, 1978.

[6] J. H. Conway and N. J. A. Sloane. Sphere packings, lattices and groups. Springer-Verlag, New York, third edition, 1999.

[7] W. Ebeling. Lattices and codes. Advanced Lectures in Mathematics. Friedr. Vieweg & Sohn, Braunschweig, revised edition, 2002.

[8] H. Inose. Defining equations of singular K3 surfaces and a notion of isogeny. In Proceedings of the International Symposium on Algebraic Geometry (Kyoto Univ., Kyoto, 1977), pages 495-502, Tokyo, 1978. Kinokuniya Book Store.

[9] V. V. Nikulin. Kummer surfaces. Izv. Akad. Nauk SSSR Ser. Mat., 39(2):278-293, 471, 1975. [OpenAIRE]

[10] V. V. Nikulin. Integer symmetric bilinear forms and some of their geometric applications. Izv. Akad. Nauk SSSR Ser. Mat., 43(1):111-177, 238, 1979. English translation: Math USSR-Izv. 14 (1979), no. 1, 103-167 (1980).

[11] V. V. Nikulin. Weil linear systems on singular K3 surfaces. In Algebraic geometry and analytic geometry (Tokyo, 1990), ICM-90 Satell. Conf. Proc., pages 138-164. Springer, Tokyo, 1991.

[12] A. Ogus. Supersingular K3 crystals. In Journ´ees de G´eom´etrie Alg´ebrique de Rennes (Rennes, 1978), Vol. II, volume 64 of Ast´erisque, pages 3-86. Soc. Math. France, Paris, 1979.

[13] A. Ogus. A crystalline Torelli theorem for supersingular K3 surfaces. In Arithmetic and geometry, Vol. II, volume 36 of Progr. Math., pages 361-394. Birkha¨user Boston, Boston, MA, 1983.

[14] A. N. Rudakov and I. R. Shafarevich. Surfaces of type K3 over fields of finite characteristic. In Current problems in mathematics, Vol. 18, pages 115-207. Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii, Moscow, 1981. Reprinted in I. R. Shafarevich, Collected Mathematical Papers, Springer-Verlag, Berlin, 1989, pp. 657-714.

[15] B. Saint-Donat. Projective models of K − 3 surfaces. Amer. J. Math., 96:602-639, 1974. [OpenAIRE]

25 references, page 1 of 2
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