Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz
Tamas Hausel
Rodríguez Villegas, Fernando
We calculate the E-polynomials of certain twisted GL(n,ℂ)-character varieties Mn of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n, q) and a theorem proved in the appendix by N. Katz. We deduce from this calculation several geometric results, for example, the value of the topological Euler characteristic of the associated PGL(n,ℂ)-character variety. The calculation also leads to several conjectures about the cohomology of Mn: an explicit conjecture for its mixed Hodge polynomial; a conjectured curious hard Lefschetz theorem and a conjecture relating the pure part to absolutely indecomposable representations of a certain quiver. We prove these conjectures for n=2.
Springer
2008
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http://purl.org/coar/resource_type/c_6501
https://research-explorer.app.ist.ac.at/record/1460
Hausel T, Rodríguez Villegas F. Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz. <i>Inventiones Mathematicae</i>. 2008;174(3):555-624. doi:<a href="https://doi.org/10.1007/s00222-008-0142-x">10.1007/s00222-008-0142-x</a>
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00222-008-0142-x
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