The cohomology ring of certain compactified Jacobians

2017/10/15 by Oblomkov, Alexei, Yun, Zhiwei · 1 citation
#14F20 #14F40 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.05391

Abstract

We provide an explicit presentation of the equivariant cohomology ring of the compactified Jacobian J_q/p of the rational curve C_q/p with planar equation x^q=y^p for (p,q)=1. We also prove analogous results for the closely related affine Springer fiber Sp_q/p in the affine flag variety of SL_p. We show that the perverse filtration on the cohomology of J_q/p is multiplicative, and the associated graded ring under the perverse filtration is a degeneration of the ring of functions on a moduli space of maps ℙ¹→ C_q/p. We also propose several conjectures about J_q/p and more general compactified Jacobians.

Cited by

• Cohomology of compactified Jacobians for locally planar integral curves

Related

• The intrinsic cohomology ring of the universal compactified Jacobian over the moduli space of stable curves
• Cohomology of compactified Jacobians for locally planar integral curves
• Cohomology of line bundles on compactified Jacobians
• Compactified jacobians
• Geometry of genus one fine compactified universal Jacobians