Generic vanishing and minimal cohomology classes on abelian varieties

2006/10/05 by Giuseppe Pareschi, Pareschi, Giuseppe, Mihnea Popa +1
Mathematics · #14F17 #14K12 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.math/0610166

openalex publication_date 2006/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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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