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|Title:||Arithmetic of singular character varieties and their E-polynomials|
|Citation:||Proceedings of the London Mathematical Society, 2017; 114(2):293-332|
|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|
|Appears in Collections:||Aurora harvest 3|
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