A characterization of finite quotients of Abelian varieties
A characterization of finite quotients of Abelian varieties
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阿贝尔簇有限商的表征
DOI：
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发表时间：
2014
期刊：
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通讯作者：
Behrouz Taji
中科院分区：
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作者：
Steven Lu;Behrouz Taji
本文利用余维1自由的有限群的作用，通过对Orbifold Chern类的消隐条件，证明了Abel簇的同分性的一个刻画。的特点是一类品种之间的温和的奇异性比商奇异性，即类之间的klt品种。此外，我们表明，在一个射影klt品种，任何半稳定的自反层消失orbifold陈类可以获得的不变部分的局部自由层的有限伽罗瓦覆盖，其相关的向量丛是平坦的。
In this paper we prove a characterization of quotients of Abelian varieties by the actions of finite groups that are free in codimension-one via some vanishing conditions on the orbifold Chern classes. The characterization is given among a class of varieties with mild singularities that are more general than quotient singularities, namely among the class of klt varieties. Furthermore we show that over a projective klt variety, any semistable reflexive sheaf with vanishing orbifold Chern classes can be obtained as the invariant part of a locally-free sheaf on a finite Galois cover whose associated vector bundle is flat.