Vector bundles on the cubic threefold

2000/05/02 by Arnaud Beauville, Beauville, Arnaud
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0005017

19 pages, TeX with xy-pic

arxiv created 2000/05/02 · arxiv updated 2009/11/30

Abstract

Let X be a smooth cubic threefold, M the moduli space of stable rank 2 vector bundles on X with trivial determinant and c₂=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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