2 8 Ju l 2 00 3 Cubic Threefolds and Abelian Varieties of Dimension Five

Cubic threefolds have been studied in algebraic geometry since classical times. In [5], Clemens and Griffiths proved that the intermediate Jacobian JX of a smooth cubic threefold is not isomorphic as a principally polarized abelian variety to a product of Jacobians of curves, which implies the irrationality of X. They also established the Torelli theorem… CONTINUE READING