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University of Cambridge > Talks.cam > Algebraic Geometry Seminar > Degenerations of cubic threefolds

## Degenerations of cubic threefoldsAdd to your list(s) Download to your calendar using vCal - Klaus Hulek (Leibniz)
- Wednesday 04 November 2015, 14:15-15:15
- CMS MR13.
If you have a question about this talk, please contact Dr. J Ross. Due to a famous result of Clemens and Griffiths a smooth cubic threefold $X$ is a unirational, but not rational variety. The key tool in their proof is the intermediate Jacobian $J(X)$, which is a principally polarized abelian 5-fold. Associating to a cubic threefold $X$ its intermediate Jacobian $J(X)$ defines a morphism $p: M_4 \to A_5$ from the moduli space $M_4$ of cubic threefolds to the moduli space $A_5$ of principally polarized abelian $5$-folds which, by the Torelli theorem, is injective. We exhibit a suitable compactification $\overline{M}_4$ of $M_4$ such that the Torelli map extends to a morphism $\overline{p}: \overline{M}_4 \to \overline{A}_5$ to the second Voronoi compactification of $A_5$. In a number of cases we can determine the effect of singularities of $X$ on the degenerate intermediate Jacobian. This is joint work with S. Casalaina-Martin, S. Grushevsky and R. Laza. This talk is part of the Algebraic Geometry Seminar series. ## This talk is included in these lists:- Algebraic Geometry Seminar
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