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摘要翻译：
在阿贝尔变种的情况下，我们描述了$M$-正则sheaf和$GV$-正则sheaf概念之间的关系。前者是后者的自然加强，我们提供了一个在较大类中刻画它的代数判据。在此基础上，我们导出了$M$-正则轮和$GV$-轮的新的基本性质。第二部分给出了$m$-正则束的生成判据在Seshadri常数、Picard束、不规则簇上的多元映射和半齐次向量束研究中的一些应用。这篇论文的第二部分是基于我们早期预印本Math.AG/0306103的，有一些改进的陈述和缩短的参数。
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英文标题：
《Regularity on abelian varieties III: relationship with Generic Vanishing
and applications》
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作者：
Giuseppe Pareschi and Mihnea Popa
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
We describe the relationship between the notions of $M$-regular sheaf and $GV$-sheaf in the case of abelian varieties. The former is a natural strengthening of the latter, and we provide an algebraic criterion characterizing it among the larger class. Based on this we deduce new basic properties of both $M$-regular and $GV$-sheaves. In the second part we give a number of applications of generation criteria for $M$-regular sheaves to the study of Seshadri constants, Picard bundles, pluricanonical maps on irregular varieties, and semihomogeneous vector bundles. This second part of the paper is based on our earlier preprint math.AG/0306103, with some improved statements and shortened arguments.
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PDF链接：
https://arxiv.org/pdf/0802.1021
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