Arithmetic of singular character varieties and their E-polynomials

作者：Baraglia David^*; Hekmati Pedram

来源：Proceedings of the London Mathematical Society, 2017, 114(2): 293-332.

DOI：10.1112/plms.12008

We calculate the E-polynomials of the SL3(C)-and GL(3)(C)-character varieties of compact oriented surfaces of any genus and the E-polynomials of the SL2(C)-and GL(2)(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, Munoz and Newstead for genus g = 1, 2 and by Martinez and Munoz 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.

• 出版日期2017-2