A characterization of finite quotients of Abelian varieties

Abstract

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.

Added more details for the arguments in the final section. To appear in International Mathematics Research Notices

References in corpus (2)

• Étale fundamental groups of Kawamata log terminal spaces, flat sheaves, and quotients of Abelian varieties
• The Miyaoka-Yau inequality and uniformisation of canonical models

Cited by in corpus (6)

• The Miyaoka-Yau inequality and uniformisation of canonical models
• Projectively flat KLT varieties
• Projective flatness over klt spaces and uniformisation of varieties with nef anti-canonical divisor
• Equality in the Miyaoka-Yau inequality and uniformization of non-positively curved klt pairs
• Uniformisation of higher-dimensional minimal varieties
• Miyaoka-Yau inequalities and the topological characterization of certain klt varieties