摘要翻译:
设$(A,\theta)$是一个主极化的阿贝尔变体,设Y是一个子变体。Pareschi和Popa猜想Y具有极小上同调类当且仅当Y的结构束满足一个他们称之为M-正则性的性质。设X是光滑的三重立方。根据Clemens和Griffiths的经典结果,它的中间雅可比J(X)是一个主要极化的阿贝尔变体;此外,X上直线的Fano曲面可以嵌入J(X)中,并具有极小上同调类。在这篇短注中,我们证明了它的结构束是m-正则的。
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英文标题:
《M-regularity of the Fano surface》
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作者:
Andreas H\"oring
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最新提交年份:
2017
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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:
Let $(A,\Theta)$ be a principally polarised abelian variety, and let Y be a subvariety. Pareschi and Popa conjectured that Y has minimal cohomology class if and only if the structure sheaf of Y satisfies a property that they call M-regularity. Let now X be a smooth cubic threefold. By a classical result due to Clemens and Griffiths, its intermediate Jacobian J(X) is a principally polarised abelian variety; furthermore the Fano surface of lines on X can be embedded in J(X) and has minimal cohomology class. In this short note we show that its structure sheaf is M-regular.
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PDF链接:
https://arxiv.org/pdf/0704.0558