Subvarieties of generic hypersurfaces in a nonsingular projective toric variety

被引：0
作者：
Atsushi Ikeda
机构：
[1] Osaka University,Graduate School of Science
来源：
Mathematische Zeitschrift | 2009年 / 263卷
关键词：
Toric variety; Generic hypersurface; Subvariety; Multiplication of linear systems; Primary 14M25; Secondary 14C20; 14J70;
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学科分类号：
摘要：
We investigate the subvarieties contained in generic hypersurfaces of projective toric varieties and prove two main theorems. The first generalizes Clemens’ famous theorem on the genus of curves in hypersurfaces of projective spaces to curves in hypersurfaces of toric varieties and the second improves the bound in the special case of toric varieties in a theorem of Ein on the positivity of subvarieties contained in sufficiently ample generic hypersurfaces of projective varieties. Both depend on a hypothesis which deals with the surjectivity of multiplication maps of sections of line bundles on the toric variety. We also obtain an infinitesimal Torelli theorem for hypersurfaces of toric varieties.
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页码：923 / 937
页数：14
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