Unirational moduli spaces of some elliptic K3 surfaces

被引：1

作者：

Fortuna, Mauro ^{[1
]}

Hoff, Michael ^{[2
]}

Mezzedimi, Giacomo ^{[1
,3
]}

机构：

[1] Leibniz Univ Hannover, Inst Algebra Geometrie, Welfengarten 1, D-30167 Hannover, Germany

[2] Univ Saarland, Campus E2 4, D-66123 Saarbrucken, Germany

[3] Univ Bonn, Math Inst, Endenicher Allee 60, D-53115 Bonn, Germany

来源：

MANUSCRIPTA MATHEMATICA | 2024年 / 173卷 / 1-2期

关键词：

WEIERSTRASS FIBRATIONS;

D O I：

10.1007/s00229-022-01455-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the moduli space of U circle plus <-2k >-polarized K3 surfaces is unirational for k <= 50 and k is not an element of{11, 35, 42, 48}, and for other several values of k up to k = 97. Our proof is based on a systematic study of the projective models of elliptic K3 surfaces in P-n for 3 <= n <= 5 containing either the union of two smooth rational curves or the union of a smooth rational curve and an elliptic curve intersecting at one point.

引用

页码：405 / 423

页数：19

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