Matrix factorizations and intermediate Jacobians of cubic threefolds

2021/12/20 by Christian Böhning, Böhning, Christian, Hans‐Christian Graf von Bothmer +2
Mathematics · #14D20 #14H40 #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.2112.10554

openalex publication_date 2021/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Results due to Druel and Beauville show that the blowup of the intermediate Jacobian of a smooth cubic threefold X in the Fano surface of lines can be identified with a moduli space of semistable sheaves of Chern classes c₁=0, c₂=2, c₃=0 on X. Here we further identify this space with a space of matrix factorizations. This has the advantage that this description naturally generalizes to singular and even reducible cubic threefolds. In this way, given a degeneration of X to a reducible cubic threefold X₀, we obtain an associated degeneration of the above moduli spaces of semistable sheaves.

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