Construction of the Poincare sheaf for higher genus curves

2018/01/08 by Lijun Mao, Li, Mao
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1801.02993

openalex publication_date 2018/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth projective curve of genus g and L be a degree l line bundle on X with l≥ 2g-1. Denote the stack of rank two Higgs bundles on X with value in L by Higgs and the semistable part by Higgs_ss. Let H be the Hitchin base. In this paper we will construct the Poincare sheaf P on Higgs×_HHiggs_ss which is a maximal Cohen-Macaulay sheaf and flat over Higgs_ss. In particular this includes the locus of nonreduced spectral curves.

Citations

• Cohomology of line bundles on compactified Jacobians
• Algebraic Families on an Algebraic Surface
• Autoduality of compactified Jacobians for curves with plane singularities
• Construction of the Poincaré sheaf on the stack of rank two Higgs bundles of P¹
• Autoduality of the compactified Jacobian

Related

• Construction of the Poincaré sheaf on the stack of rank two Higgs bundles of P¹
• The Poincare line bundle and autoduality of Hitchin fibers
• Indecomposable vector bundles and stable Higgs bundles over smooth\n projective curves
• Higher rank Clifford's theorem on the smooth quadric
• Sheaves on non-reduced curves in a projective surface