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Vector bundles on the cubic threefold

Arnaud Beauville
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Abstract

Let X be a smooth cubic threefold, M the moduli space of stable rank 2 vector bundles on X with trivial determinant and c_2=2 (the smallest value for which this space is non-empty). Recent results of Druel, Iliev, Markushevich and Tikhomirov lead to a precise description of M and its Maruyama compactification M': the latter is isomorphic to the intermediate Jacobian of X blown-up along the Fano surface. In this survey paper we explain these results and discuss some applications.

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Arnaud Beauville. 2000-05-02. Vector bundles on the cubic threefold. https://arxiv.org/abs/math/0005017

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