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Type: Journal article
Title: Arithmetic of singular character varieties and their E-polynomials
Author: Baraglia, D.
Hekmati, P.
Citation: Proceedings of the London Mathematical Society, 2017; 114(2):293-332
Publisher: Wiley
Issue Date: 2017
ISSN: 0024-6115
Statement of
David Baraglia and Pedram Hekmati
Abstract: We calculate the E-polynomials of the SL₃(C)- and GL₃(C)-character varieties of compact oriented surfaces of any genus and the E-polynomials of the SL₂(C)- and GL₂(C)-character varieties of compact non-orientable surfaces of any Euler characteristic. Our methods also give a new and significantly simpler computation of the E-polynomials of the SL₂(C)-character varieties of compact orientable surfaces, which were computed by Logares, Muñoz and Newstead for genus g = 1, 2 and by Martinez and Muñoz for g ⩾3. Our technique is based on the arithmetic of character varieties over finite fields. More specifically, we show how to extend the approach of Hausel and Rodriguez-Villegas used for non-singular (twisted) character varieties to the singular (untwisted) case.
Rights: © 2017 London Mathematical Society
DOI: 10.1112/plms.12008
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Mathematical Sciences publications

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