Arithmetic of singular character varieties and their E-polynomials
Date
2017
Authors
Baraglia, D.
Hekmati, P.
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Journal article
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Proceedings of the London Mathematical Society, 2017; 114(2):293-332
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David Baraglia and Pedram Hekmati
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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.
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© 2017 London Mathematical Society