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arXiv · 2112.10554

Matrix factorizations and intermediate Jacobians of cubic threefolds

Christian Böhning·Hans-Christian Graf von Bothmer·Lukas Buhr
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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 c_1=0, c_2=2, c_3=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 X_0, we obtain an associated degeneration of the above moduli spaces of semistable sheaves.

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Christian Böhning, Hans-Christian Graf von Bothmer, Lukas Buhr. 2021-12-20. Matrix factorizations and intermediate Jacobians of cubic threefolds. https://arxiv.org/abs/2112.10554

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