Anticanonical divisors and curve classes on Fano manifolds
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 Andreas Hoering (Jussieu)
 Wednesday 17 October 2012, 14:1515:15
 MR 13, CMS.
If you have a question about this talk, please contact Caucher Birkar.
Let X be a Fano manifold, i.e. a projective complex manifold such that K_X is ample.
If X has dimension three a classical but nontrivial result by Shokurov says that a general
element in the
anticanonical system K_X is a smooth surface. In higher dimension the situation is much more
complicated,
we prove that for a fourfold a general anticanonical divisor has at most isolated singularities.
As an application we obtain
an integral version of the Hodge conjecture : for a Fano fourfold the group H^6(X, Z) is
generated over Z by classes of curves.
This is joint work with Claire Voisin.
This talk is part of the Algebraic Geometry Seminar series.
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