Intersection cohomology of rank two character varieties of surface groups

Abstract

For $G={\mathrm{GL}}_2,{\mathrm{SL}}_2,{\mathrm{PGL}}_2$ we compute the intersection E-polynomials and the intersection Poincaré 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.

arXiv comment44 pages. Comments are welcome!

References in corpus (11)

• Mirror symmetry, Langlands duality, and the Hitchin system
• Lectures on Nakajima's Quiver Varieties
• An overview of Morihiko Saito's theory of mixed Hodge modules
• Global topology of the Hitchin system
• On the E-polynomials of a family of Character Varieties
• Arithmetic of singular character varieties and their $E$-polynomials
• Hitchin fibrations, abelian surfaces, and the P=W conjecture
• Cell decompositions of character varieties
• On the P=W conjecture for ${\mathrm{SL}}_n$
• Symplectic resolutions of character varieties
• Intersection cohomology of moduli spaces of vector bundles over curves

Cited by in corpus (1)

• Purity and 2-Calabi-Yau categories