Poincaré polynomials of moduli spaces of Higgs bundles and character varieties (no punctures)

By Anton Mellit. Inventiones Mathematicae, 2017

56 citations recorded by the source corpus.

Using our earlier results on polynomiality properties of plethystic logarithms of generating series of certain type, we show that Schiffmann’s formulas for various counts of Higgs bundles over finite fields can be reduced to much simpler formulas conjectured by Mozgovoy. In particular, our result implies the conjecture of Hausel and Rodriguez-Villegas on the Poincaré polynomials of twisted character varieties and the conjecture of Hausel and Thaddeus on independence of E-polynomials on the degree.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6796033b52b9cba7a047d99150035be131d4609e

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In Algebra and Number Theory

1. Junliang Shen
2. Davesh Maulik

In Geometry and Topology

1. Junliang Shen
2. Davesh Maulik
3. R. Pandharipande
4. D. Huybrechts
5. A. Okounkov
6. Franccois Charles
7. A. Zinger
8. Richard P. Thomas

In Mathematical Physics

1. Junliang Shen
2. Davesh Maulik
3. R. Pandharipande
4. D. Huybrechts
5. Franccois Charles
6. A. Okounkov
7. A. Zinger
8. C. Liedtke

Citations in the corpus

• Cohomological χ–independence for moduli of one-dimensional sheaves and moduli of Higgs bundles (2020, methodology): “[36] A. Mellit, Poincaré polynomials of moduli spaces of Higgs bundles and character varieties (no punctures), Invent.”