Mixed Hodge polynomials of character varieties
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 geo...
| Үндсэн зохиолчид: | , |
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| Формат: | Journal article |
| Хэвлэсэн: |
2006
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| _version_ | 1826305034629939200 |
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| author | Hausel, T Rodriguez-Villegas, F |
| author_facet | Hausel, T Rodriguez-Villegas, F |
| author_sort | Hausel, T |
| collection | OXFORD |
| 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. |
| first_indexed | 2024-03-07T06:26:44Z |
| format | Journal article |
| id | oxford-uuid:f48eb3db-4fc3-449f-94b1-2d3f3622706d |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:26:44Z |
| publishDate | 2006 |
| record_format | dspace |
| spelling | oxford-uuid:f48eb3db-4fc3-449f-94b1-2d3f3622706d2022-03-27T12:20:41ZMixed Hodge polynomials of character varietiesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f48eb3db-4fc3-449f-94b1-2d3f3622706dSymplectic Elements at Oxford2006Hausel, TRodriguez-Villegas, FWe 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. |
| spellingShingle | Hausel, T Rodriguez-Villegas, F Mixed Hodge polynomials of character varieties |
| title | Mixed Hodge polynomials of character varieties |
| title_full | Mixed Hodge polynomials of character varieties |
| title_fullStr | Mixed Hodge polynomials of character varieties |
| title_full_unstemmed | Mixed Hodge polynomials of character varieties |
| title_short | Mixed Hodge polynomials of character varieties |
| title_sort | mixed hodge polynomials of character varieties |
| work_keys_str_mv | AT hauselt mixedhodgepolynomialsofcharactervarieties AT rodriguezvillegasf mixedhodgepolynomialsofcharactervarieties |