Topology of Hitchin systems and Hodge theory of character varieties
By M. A. Cataldo, Tamás Hausel, L. Migliorini. 2010
188 citations recorded by the source corpus.
For G = GL2; PGL2; SL2 we prove that the perverse ltration associated with the Hitchin map on the rational cohomology of the moduli space of twisted G-Higgs bundles on a compact Riemann surface C agrees with the weight ltration on the rational cohomology of the twisted G character variety of C when the cohomologies are identied via non-Abelian Hodge theory. The proof is accomplished by means of a study of the topology of the Hitchin map over the locus of integral spectral curves.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/61734c8dcf5a9f580b7dd002bce2866c645af34a
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In Geometry and Topology
- Junliang Shen
- Andrei Neguct
- Davesh Maulik
- M. A. Cataldo
- E. Gorsky
- R. Pandharipande
- L. Migliorini
- D. Huybrechts
In Mathematical Physics
- Davesh Maulik
- Junliang Shen
- Andrei Neguct
- M. A. Cataldo
- E. Gorsky
- R. Pandharipande
- L. Migliorini
- D. Huybrechts
Citations in the corpus
- Refined knot invariants and Hilbert schemes (2013, background): “In [8] de Cataldo, Hausel and Migliorini conjectured that the Hodge filtration in the cohomology of the character variety matches the perverse filtration in the cohomology of the corresponding Hitchin moduli space and proved this conjecture in A1 case.”
- Hitchin fibrations, abelian surfaces, and the P=W conjecture (2019, background): “A striking prediction, suggested by the parallel between the Relative Hard Lefschetz [7] and Curious Hard Lefschetz [29] Theorems, was suggested by de Cataldo, Hausel, and Migliorini [13]; it predicts that the perverse filtration of MDol with respect to the Hitchin fibration (2) matches the weight f”