Fourier transforms, generic vanishing theorems and polarizations of abelian varieties

Abstract

The purpose of this paper is to give two applications of Fourier transforms and generic vanishing theorems: – we give a cohomological characterization of principal polarizations – we prove that if X an abelian variety and $\Theta $ a polarization of type (1, ...,1,2), then a general pair $(X,\Theta )$ is log canonical.