Cohomology of compactified Jacobians for locally planar integral curves

2025/12/17 by Shen, Junliang
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.2512.14995

Abstract

This article surveys some recent developments on the cohomology of the compactified Jacobian associated with a locally planar integral curve. Topics discussed here include the Ngô support theorem, the perverse filtration, connections to the Hilbert schemes, and cohomological structures induced by the Arinkin-Fourier-Mukai transform.

Citations

• Stabilization of intersection Betti numbers for moduli spaces of one-dimensional sheaves on surfaces
• The intrinsic cohomology ring of the universal compactified Jacobian over the moduli space of stable curves
• On the Perversity of Chern Classes for Compactified Jacobians
• Degree two Gopakumar-Vafa invariants of local curves
• Cohomological stabilization, perverse filtrations, and refined BPS invariants for del Pezzo surfaces
• On generalized Beauville decompositions
• The Hilb-vs-Quot Conjecture
• Perverse filtrations and Fourier transforms
• Non-abelian Hodge moduli spaces and homogeneous affine Springer fibers
• Combinatorial decomposition theorem for Hitchin systems via zonotopes
• Hodge-to-singular correspondence for reduced curves
• From the Hecke Category to the Unipotent Locus
• Hitchin fibrations, abelian surfaces, and the P=W conjecture
• The cohomology ring of certain compactified Jacobians
• Gopakumar-Vafa invariants via vanishing cycles
• The weights of the tautological classes of character varieties
• Geometric representations of graded and rational Cherednik algebras
• Un théorème du support pour la fibration de Hitchin
• Homology of Hilbert schemes of points on a locally planar curve
• Stable pairs and the HOMFLY polynomial
• HOMFLY polynomials, stable pairs and motivic Donaldson-Thomas invariants
• Macdonald formula for curves with planar singularities
• Topology of Hitchin systems and Hodge theory of character varieties: the case A₁
• Autoduality of compactified Jacobians for curves with plane singularities
• The perverse filtration and the Lefschetz hyperplane theorem, II
• The Hodge theory of algebraic maps
• Fibres de Springer et jacobiennes compactifiees

Related

• The cohomology ring of certain compactified Jacobians
• Cohomology of line bundles on compactified Jacobians
• Autoduality of compactified Jacobians for curves with plane singularities
• Macdonald formula for curves with planar singularities
• The intrinsic cohomology ring of the universal compactified Jacobian over the moduli space of stable curves