Intersection cohomology of rank two character varieties of surface groups

Mirko Mauri

Intersection cohomology of rank two character varieties of surface groups

Algebraic Geometry 2021-01-13 v1 Representation Theory

Authors: Mirko Mauri

Abstract

For $G = \mathrm{GL}_2, \mathrm{SL}_2, \mathrm{PGL}_2$ we compute the intersection E-polynomials and the intersection Poincar\'e polynomials of the $G$ -character variety of a compact Riemann surface $C$ and of the moduli space of $G$ -Higgs bundles on $C$ of degree zero. We derive several results concerning the P=W conjectures for these singular moduli spaces.

Keywords

intersection cohomology character variety higgs bundles moduli space e-polynomial poincaré polynomial p=w conjecture

Cite

@article{arxiv.2101.04628,
  title  = {Intersection cohomology of rank two character varieties of surface groups},
  author = {Mirko Mauri},
  journal= {arXiv preprint arXiv:2101.04628},
  year   = {2021}
}

Comments

44 pages. Comments are welcome!

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