A Characterization of Finite Quotients of Abelian Varieties

作者：Lu Steven; Taji Behrouz^*

来源：International Mathematics Research Notices, 2018, (1): 292-319.

DOI：10.1093/imrn/rnw251

We provide a characterization of quotients of Abelian varieties by finite groups actions that are free in codimension-one via vanishing conditions on the orbifold Chern classes. The characterization is given among a class of varieties with singularities that are more general than quotient singularities, namely among the class of klt varieties. Furthermore, for a semistable (respectively stable) reflexive O-X-module E with zero first and second orbifold Chern classes over such a variety X, we show that E vertical bar X-reg(an) is locally-free and flat, given by a linear (irreducible unitary) representation of pi(1)(X-reg), and that it extends over a finite Galois cover (X) over tilde of X etale over X-reg to a locally-free and flat sheaf given by an equivariant linear (irreducible unitary) representation of pi(1)((X) over tilde). These are generalizations to the singular setting that is more general than any orbifold strengthenings of the classical correspondences of Donaldson-Uhlenbeck-Yau-Simpson.

• 出版日期2018-1
• 单位西北大学