On the computation of the Picard group for K3 surfaces

被引：14

作者：

Elsenhans, Andreas-Stephan ^{[1
]}

Jahnel, Joerg ^{[2
]}

机构：

[1] Univ Bayreuth, Math Inst, D-95440 Bayreuth, Germany

[2] Univ Siegen, Fachbereich Math 6, D-57068 Siegen, Germany

来源：

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | 2011年 / 151卷

关键词：

D O I：

10.1017/S0305004111000326

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a method to construct examples of K3 surfaces of geometric Picard rank 1. Our approach is a refinement of that of R. van Luijk. It is based on an analysis of the Galois module structure on etale cohomology. This allows us to abandon the original limitation to cases of Picard rank 2 after reduction modulo p. Furthermore, the use of Galois data enables us to construct examples that require significantly less computation time.

引用

页码：263 / 270

页数：8

共 16 条

[1]

[Anonymous], 1984, COMPACT COMPLEX SURF

[2]

BEAUVILLE A, 1978, ASTERISQUE, V54

[3]

Deligne P., 1974, PUBL MATH-PARIS, V43, P273, DOI 10.1007/BF02684373

[4]

Elsenhans A.-S., DISCRIMINANT CUBIC S

[5]

Elsenhans AS, 2008, LECT NOTES COMPUT SC, V5011, P212, DOI 10.1007/978-3-540-79456-1_14

[6] Cubic surfaces with a Galois invariant double-six [J].

Elsenhans, Andreas-Stephan ;

Jahnel, Joerg .

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2010, 8 (04) :646-661

[7]

ELSENHANS AS, INT J NUMBER THEORY

[8]

Fulton W., 1998, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics, Vsecond

[9] Elliptic K3 surfaces with geometric Mordell-Weil rank 15 [J].

Kloosterman, Remke .

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2007, 50 (02) :215-226

[10] NUMERICAL AND HOMOLOGICAL EQUIVALENCE OF ALGEBRAIC CYCLES ON HODGE MANIFOLDS [J].

LIEBERMAN, DI .

AMERICAN JOURNAL OF MATHEMATICS, 1968, 90 (02) :366-+

← 1 2 →