, Volume 340, Issue 1, pp 209-222
Date: 28 Jul 2007

Generic vanishing and minimal cohomology classes on abelian varieties

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Abstract

We establish a—and conjecture further—relationship between the existence of subvarieties representing minimal cohomology classes on principally polarized abelian varieties, and the generic vanishing of the cohomology of twisted ideal sheaves. The main ingredient is the Generic Vanishing criterion established in Pareschi G. and Popa M. (GV-sheaves, Fourier–Mukai transform, and Generic Vanishing. Preprint math.AG/0608127), based on the Fourier–Mukai transform.

MP was partially supported by the NSF grant DMS 0500985 and by an AMS Centennial Fellowship.