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SUMMARY:Degenerations of cubic threefolds - Klaus Hulek (Leibniz)
DTSTART:20151104T141500Z
DTEND:20151104T151500Z
UID:TALK60237@talks.cam.ac.uk
CONTACT:Dr. J Ross
DESCRIPTION: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  principa
 lly polarized abelian 5-fold. Associating to a cubic threefold  $X$ its in
 termediate 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 princ
 ipally polarized abelian $5$-folds which\, by the  Torelli theorem\, is in
 jective.\n\nWe exhibit a suitable compactification $\\overline{M}_4$ of $M
 _4$ such  that the Torelli map extends to\na morphism $\\overline{p}: \\ov
 erline{M}_4 \\to \\overline{A}_5$ to the  second Voronoi compactification 
 of $A_5$. In a number of cases we can  determine the effect of singulariti
 es of $X$ on the degenerate  intermediate Jacobian. This is joint work wit
 h S. Casalaina-Martin\, S.  Grushevsky and R. Laza.\n\n
LOCATION:CMS MR13
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