Generic vanishing and minimal cohomology classes on abelian varieties

Details Generic vanishing and minimal cohomology classes on abelian varieties Generic vanishing and minimal cohomology classes on abelian varieties

2006-10-05

arxiv.org/abs/math/0610166v2

Mathematics

Algebraic Geometry

12 pages; final version, to appear in Math. Annalen; contains expository changes and a proof in the case of abelian varieties

Scientific paper

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 certain sheaf cohomology. The
main ingredient is the Generic Vanishing criterion of math.AG/0608127, based on
the Fourier-Mukai transform.

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