Cohomology rings of character varieties

Fuente: arXiv
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Autore principale: Mellit, Anton
Natura: Preprint
Pubblicazione: 2025
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author Mellit, Anton
author_facet Mellit, Anton
contents In this talk I give an introduction and present some recent progress towards understanding the cohomology rings of character varieties of Riemann surfaces, such as the proof of the $P=W$ conjecture and the computation of the zero-dimensional COHA. In the case of punctured sphere I present an explicit description relating the cohomology rings to the Hilbert scheme of $\mathbb{C}^2$, refining conjectures of Hausel-Letellier-Rodriguez-Villegas and Chuang-Diaconescu-Donagi-Pantev. I explain how the general case should be related to the symplectic geometry of the Hilbert scheme.
format Preprint
id arxiv_https___arxiv_org_abs_2507_12454
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Cohomology rings of character varieties
Mellit, Anton
Algebraic Geometry
Representation Theory
In this talk I give an introduction and present some recent progress towards understanding the cohomology rings of character varieties of Riemann surfaces, such as the proof of the $P=W$ conjecture and the computation of the zero-dimensional COHA. In the case of punctured sphere I present an explicit description relating the cohomology rings to the Hilbert scheme of $\mathbb{C}^2$, refining conjectures of Hausel-Letellier-Rodriguez-Villegas and Chuang-Diaconescu-Donagi-Pantev. I explain how the general case should be related to the symplectic geometry of the Hilbert scheme.
title Cohomology rings of character varieties
topic Algebraic Geometry
Representation Theory
url https://arxiv.org/abs/2507.12454