Cohomology jump loci in the moduli spaces of vector bundles

2012/10/04 by Botong Wang, Wang, Botong
Mathematics · #14B12 #14D20 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14B12 #msc:14D20

paper · pdf · doi:10.48550/arxiv.1210.1487

arxiv created 2012/10/04 · arxiv updated 2012/10/05

Abstract

Two decades ago, as part of their work of generic vanishing theorems, Green-Lazarsfeld showed that over a compact Kahler manifold X, the cohomology jump loci in the Pic^τ(X) are all translates of subtori. In this paper, we generalize this result to higher dimensional vector bundles. It is showed by Nadel that locally the moduli space of vector bundles with vanishing chern classes is canonically isomorphic to a quadratic cone in the Zariski tangent space of a point. We prove that under the isomorphism, the cohomology jump loci are defined by linear equations.

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