SEVERI VARIETIES AND SELF-RATIONAL MAPS OF K3 SURFACES

被引：10
作者：
Dedieu, Thomas [1 ]
机构：
[1] Univ Paris 06, Inst Math Jussieu, Equipe Topol & Geometrie Algebr, UMR 7586, F-75013 Paris, France
来源：
INTERNATIONAL JOURNAL OF MATHEMATICS | 2009年 / 20卷 / 12期
关键词：
Severi varieties; self-rational maps; K3; surfaces; CURVES; FAMILIES; NUMBER;
D O I：
10.1142/S0129167X09005844
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Self-rational maps of generic algebraic K3 surfaces are conjectured to be trivial. We relate this conjecture to a conjecture concerning the irreducibility of the universal Severi varieties parameterizing nodal curves of given genus and degree lying on some K3 surface. We also establish a number of numerical constraints satisfied by such nontrivial rational maps, that is of topological degree > 1.
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收藏
页码：1455 / 1477
页数：23
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