Cohomology of compactified Jacobians for locally planar integral curves

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.

24 pages, revision with several corrections. Accepted version at the Bootcamp Proceedings for the 2025 Summer Research Institute in Algebraic Geometry