E-polynomials of character varieties
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| Verfasser: | |
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| Format: | artículo original |
| Status: | Versión publicada |
| Publikationsdatum: | 2026 |
| Beschreibung: | This manuscript contains the basic ideas and constructions about e-polynomials in character varieties and the state of the art of certain research in the field, plus some new directions. We introduce mixed Hodge structures and E-polynomials, together with a series of arithmetic (counting points over finite fields) and geometric (stratification into parabolic types) techniques to compute them. We include a complete example of the calculation of the e-polynomial for the GL3-character variety of the free group. Finally, we extend the geometric stratification into parabolic types to a general reductive group G to obtain explicit motivic expressions for the G-character varieties, and reduce certain topological mirror symmetry conjectures for these moduli spaces. |
| Land: | Portal de Revistas UCR |
| Institution: | Universidad de Costa Rica |
| Repositorio: | Portal de Revistas UCR |
| Sprache: | Inglés |
| OAI Identifier: | oai:portal.revistas.ucr.ac.cr:article/3720 |
| Online Zugang: | https://revistas.ucr.ac.cr/index.php/rmatematica/article/view/3720 |
| Stichwort: | Character varieties E-polynomials Mixed Hodge structures Topological mirror symmetry Langlands duality Variedades de caracteres e-polinomios Estructuras de Hodge mixtas Simetría especular topológica Dualidad de Langlands |