Mixed Hodge polynomials of character varieties
| dc.creator | Hausel, Tamas | |
| dc.creator | Rodriguez-Villegas, Fernando | |
| dc.date | 2006-12-21 | |
| dc.date | 2008-05-07 | |
| dc.date.accessioned | 2026-07-07T09:37:22Z | |
| dc.date.available | 2026-07-07T09:37:22Z | |
| dc.description | We calculate the E-polynomials of certain twisted GL(n,C)-character varieties M_n of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n,F_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 M_n: 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. | |
| dc.description | with an appendix by Nicholas M. Katz; 57 pages. revised version: New definition for homogeneous weight in Definition 4.1.6, subsequent arguments modified. Some other minor changes. To appear in Invent. Math | |
| dc.identifier | https://arxiv.org/abs/math/0612668 | |
| dc.identifier | http://arxiv.org/abs/math/0612668 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160436 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | Symplectic Geometry | |
| dc.title | Mixed Hodge polynomials of character varieties | |
| dc.type | text |