Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2017
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/1711.07909 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929330388467712 |
|---|---|
| author | Florentino, Carlos A. Silva, Jaime A. M. |
| author_facet | Florentino, Carlos A. Silva, Jaime A. M. |
| contents | Let F be a finite group and X be a complex quasi-projective F-variety. For r in N, we consider the mixed Hodge-Deligne polynomials of quotients X^r/F, where F acts diagonally, and compute them for certain classes of varieties X with simple mixed Hodge structures. A particularly interesting case is when X is the maximal torus of an affine reductive group G, and F is its Weyl group. As an application, we obtain explicit formulae for the Hodge-Deligne and E-polynomials of (the distinguished component of) G-character varieties of free abelian groups. In the cases G=GL(n,C) and SL(n,C) we get even more concrete expressions for these polynomials, using the combinatorics of partitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1711_07909 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Hodge-Deligne polynomials of character varieties of abelian groups Florentino, Carlos A. Silva, Jaime A. M. Algebraic Geometry 32S35, 20C30, 14L30 Let F be a finite group and X be a complex quasi-projective F-variety. For r in N, we consider the mixed Hodge-Deligne polynomials of quotients X^r/F, where F acts diagonally, and compute them for certain classes of varieties X with simple mixed Hodge structures. A particularly interesting case is when X is the maximal torus of an affine reductive group G, and F is its Weyl group. As an application, we obtain explicit formulae for the Hodge-Deligne and E-polynomials of (the distinguished component of) G-character varieties of free abelian groups. In the cases G=GL(n,C) and SL(n,C) we get even more concrete expressions for these polynomials, using the combinatorics of partitions. |
| title | Hodge-Deligne polynomials of character varieties of abelian groups |
| topic | Algebraic Geometry 32S35, 20C30, 14L30 |
| url | https://arxiv.org/abs/1711.07909 |