Examples of topological spaces with arbitrary cohomology jump loci

Botong Wang

Examples of topological spaces with arbitrary cohomology jump loci

Algebraic Geometry 2013-04-04 v2 Algebraic Topology

Authors: Botong Wang

Abstract

Given any subvariety of a complex torus defined over $\mathbb{Z}$ and any positive integer $k$ , we construct a finite CW complex $X$ such that the $k$ -th cohomology jump locus of $X$ is equal to the chosen subvariety, and the $i$ -th cohomology jump loci of $X$ are trivial for $i<k$ .

Keywords

topological spaces cohomology jump loci complex torus CW complex subvariety algebraic geometry

Cite

@article{arxiv.1304.0239,
  title  = {Examples of topological spaces with arbitrary cohomology jump loci},
  author = {Botong Wang},
  journal= {arXiv preprint arXiv:1304.0239},
  year   = {2013}
}

Comments

Carlos Simpson has kindly pointed out to us that the main idea of this paper has been considered in his 1997 survey paper, at least for the case when $k=2$. This is added to the introduction

Examples of topological spaces with arbitrary cohomology jump loci

Abstract

Keywords

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