Hitchin fibrations, abelian surfaces, and the P=W conjecture

DOI10.1090/jams/989OpenAlexW3212729088WikidataQ113823101 ScholiaQ113823101MaRDI QIDQ5864299

Mark Andrea A. De Cataldo, Davesh Maulik, Junliang Shen

Publication date: 7 June 2022

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.11885

Mathematics Subject Classification ID

Algebraic moduli problems, moduli of vector bundles (14D20) Vector bundles on curves and their moduli (14H60) Topological properties in algebraic geometry (14F45)

Related Items

INTERSECTION COHOMOLOGY OF THE MODULI SPACE OF HIGGS BUNDLES ON A GENUS 2 CURVE, P=W conjectures for character varieties with symplectic resolution, Deformations of compact Prym fibrations to Hitchin systems, Intersection cohomology of character varieties for punctured Riemann surfaces, Perverse filtrations, Chern filtrations, and refined BPS invariants for local \(\mathbb{P}^2\), E-polynomials of character varieties for real curves, INTERSECTION COHOMOLOGY OF RANK 2 CHARACTER VARIETIES OF SURFACE GROUPS, Cohomological \(\chi\)-independence for moduli of one-dimensional sheaves and moduli of Higgs bundles, On the \(P = W\) conjecture for \(\mathrm{SL}_n\), Maximal variation of curves on \(K3\) surfaces, On intersection cohomology and Lagrangian fibrations of irreducible symplectic varieties, Lagrangian fibrations

Cites Work

• Topology of Hitchin systems and Hodge theory of character varieties: the case \(A_1\)
• Multiplicativity of perverse filtration for Hilbert schemes of fibered surfaces
• Stable bundles and integrable systems
• Density properties for certain subgroups of semi-simple groups without compact components
• Integral generators for the cohomology ring of moduli spaces of sheaves over Poisson surfaces
• Mixed Hodge polynomials of character varieties. With an appendix by Nicholas M. Katz.
• The Betti numbers of the Hilbert scheme of points on a smooth projective surface
• Tresses, monodromie et le groupe symplectique
• Higgs bundles and local systems
• Riemann-Roch for singular varieties
• Perverse sheaves and the cohomology of Hilbert schemes of smooth algebraic surfaces
• Gopakumar-Vafa invariants via vanishing cycles
• Moduli of representations of the fundamental group of a smooth projective variety. II
• The Chow groups and the motive of the Hilbert scheme of points on a surface
• On the image of MRC fibrations of projective manifolds with semi-positive holomorphic sectional curvature
• Generators of the cohomology ring of moduli spaces of sheaves on symplectic surfaces
• BPS states and the P=W conjecture
• The Hodge theory of algebraic maps
• Hodge-theoretic aspects of the Decomposition Theorem
• The decomposition theorem, perverse sheaves and the topology of algebraic maps
• Spectral curves and the generalised theta divisor.
• The Weights of the Tautological Classes of Character Varieties
• Generators for the cohomology ring of the moduli space of rank 2 Higgs bundles
• Perverse filtrations, Hilbert schemes, and the $P=W$ Conjecture for parabolic Higgs bundles
• P = W for Lagrangian fibrations and degenerations of hyper-Kähler manifolds
• Lagrangian Fibrations of Holomorphic-Symplectic Varieties of K3[n-Type]
• On the monodromy of moduli spaces of sheaves on K3 surfaces
• Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces
• Hodge-theoretic splitting mechanisms for projective maps
• Moduli spaces of stable sheaves on abelian surfaces.
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