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Character varieties with Zariski closures of GL_n-conjugacy classes at punctures
Algebraic Geometry · Submitted 29 Sep 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In this paper we extend the above results to character varieties with Zariski closures of arbitrary generic conjugacy classes at punctures working with intersection cohomology.
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The abstract, sentence by sentence
In a previous paper (joint with Hausel and Rodriguez-Villegas) we gave a conjectural formula for the mixed Hodge polynomials of character varieties with generic semisimple conjugacy classes at punctures and we prove a formula for the E-polynomial. We also proved that these character varieties are irreducible. In this paper we extend the above results to character varieties with Zariski closures of arbitrary generic conjugacy classes at punctures working with intersection cohomology. We also study Weyl group action on the intersection cohomology of the partial resolutions of these character varieties and give a conjectural formula for the two-variables polynomials that encode the trace of the elements of the Weyl group on the subquotients of the weight filtration. Finally, we compute the generating function of the stack count of character varieties with Zariski closure of unipotent regular conjugacy class at punctures.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In a previous paper (joint with Hausel and Rodriguez-Villegas) we gave a conjectural formula for the mixed Hodge polynomials of character varieties with generic semisimple conjugacy classes at punctures and we prove a formula for the E-polynomial. | background 0.99 | 0.68 | 0.07 | asserted 0.92 |
| s1 | We also proved that these character varieties are irreducible. | background 0.52 | 0.74 | 0.06 | asserted 1.00 |
| s2 | In this paper we extend the above results to character varieties with Zariski closures of arbitrary generic conjugacy classes at punctures working with intersection cohomology. | contribution 1.00 | 0.90 | 0.58 | asserted 0.99 |
| s3 | We also study Weyl group action on the intersection cohomology of the partial resolutions of these character varieties and give a conjectural formula for the two-variables polynomials that encode the trace of the elements of the Weyl group on the subquotients of the weight filtration. | contribution 0.87 | 0.94 | 0.13 | asserted 0.56 |
| s4 | Finally, we compute the generating function of the stack count of character varieties with Zariski closure of unipotent regular conjugacy class at punctures. | result 0.94 | 0.95 | 0.14 | asserted 1.00 |
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The paper
Original abstract
In a previous paper (joint with Hausel and Rodriguez-Villegas) we gave a conjectural formula for the mixed Hodge polynomials of character varieties with generic semisimple conjugacy classes at punctures and we prove a formula for the E-polynomial. We also proved that these character varieties are irreducible. In this paper we extend the above results to character varieties with Zariski closures of arbitrary generic conjugacy classes at punctures working with intersection cohomology. We also study Weyl group action on the intersection cohomology of the partial resolutions of these character varieties and give a conjectural formula for the two-variables polynomials that encode the trace of the elements of the Weyl group on the subquotients of the weight filtration. Finally, we compute the generating function of the stack count of character varieties with Zariski closure of unipotent regular conjugacy class at punctures.
Human review
How the literature uses it
3 arXiv papers cite this in 6 sentences
Papers citing it · 2 sentences without a confident label
Cites it as background 3 papers
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The number of factorizations $g=t_1 t_2 ⋯t_ℓ$ where $t_1,…,t_ℓ,g$ come from specified $GL_n(_q)$ conjugacy classes $C_1,…,C_ℓ,C_ℓ+1$ appears in work of Hausel, Letellier, and Rodriguez-Villegas [ref] and more recently Letellier [ref] .
Reflection factorizations of Singer cycles · The approach of Hausel, Letellier, and Rodriguez-Villegas · 0.93
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In recent years there has been many new results concerning the $E$-polynomial of twisted character varieties: [ref] , [ref] , [ref] , [ref] and [ref] .
E-polynomial of SL(2,C)-Character Varieties of Free groups · Introduction · 1.00
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There have been several approaches from different viewpoints to this question, by using arithmetic methods for character varieties [ref] , and by using arithmetic and/or motivic methods for Higgs bundles [ref] .
Twisted spectral correspondence and torus knots · Introduction · 0.99
What it cites · 1 sentence without a confident label
Cites as background 3 papers
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The cohomology of the $_n$ (or $SL_n$)- character varieties $_B^d$ and $_Dol^d$ has been the object of a very intensive study in the literature starting from Hitchin [ref] until recent work by Hausel-Villegas [ref] , de Cataldo-Hausel-Miggliorini [ref] , Logares-Muñoz-Newstead [ref] , Garcia-Prada, Heinloth, Schmitt [ref] and Chaudouard-Laumon [ref] .
On the motives of moduli of chains and Higgs bundles · Computing the cohomology of character varieties: State of the art · 0.99
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The cohomology of the $_n$ (or $SL_n$)- character varieties $_B^d$ and $_Dol^d$ has been the object of a very intensive study in the literature starting from Hitchin [ref] until recent work by Hausel-Villegas [ref] , de Cataldo-Hausel-Miggliorini [ref] , Logares-Muñoz-Newstead [ref] , Garcia-Prada, Heinloth, Schmitt [ref] and Chaudouard-Laumon [ref] .
Hodge-Deligne polynomials of SL(2,C)-character varieties for curves of small genus · Computing the cohomology of character varieties: State of the art · 0.99
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The cohomology of the $_n$ (or $SL_n$)- character varieties $_B^d$ and $_Dol^d$ has been the object of a very intensive study in the literature starting from Hitchin [ref] until recent work by Hausel-Villegas [ref] , de Cataldo-Hausel-Miggliorini [ref] , Logares-Muñoz-Newstead [ref] , Garcia-Prada, Heinloth, Schmitt [ref] and Chaudouard-Laumon [ref] .
Sur le comptage des fibr\'es de Hitchin nilpotents · Computing the cohomology of character varieties: State of the art · 0.99
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