Cohomology of line bundles on compactified Jacobians

2007/05/02 by D. Arinkin, Arinkin, D. · 3 citations
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #14H20 #14H40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0705.0190

openalex publication_date 2007/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let C be an integral projective curve with surficial singularities. We prove that topologically trivial line bundles on the compactified Jacobian of C are in one-to-one correspondence with line bundles on C (the autoduality conjecture), and compute the cohomology of the line bundles. We also show that the natural Fourier-Mukai functor between the derived categories of quasi-coherent sheaves on the Jacobian and on the compactified Jacobian is fully faithful.

Citations

• Euler number of the compactified Jacobian and multiplicity of rational curves

Cited by

• Cohomology of vector bundles on the moduli space of parabolic connections on ℙ¹ minus 5 points
• On the Perversity of Chern Classes for Compactified Jacobians
• Construction of the Poincaré sheaf on the stack of rank two Higgs bundles of P¹

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• Autoduality of compactified Jacobians for curves with plane singularities
• Cohomology of compactified Jacobians for locally planar integral curves
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• Cohomology and Obstructions II: Curves on K-trivial threefolds