Vector bundles on the cubic threefold

Details Vector bundles on the cubic threefold Vector bundles on the cubic threefold

2000-05-02

arxiv.org/abs/math/0005017v1

Mathematics

Algebraic Geometry

19 pages, TeX with xy-pic

Scientific paper

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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