Anticanonical divisors and curve classes on Fano manifolds

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• Andreas Hoering (Jussieu)
• Wednesday 17 October 2012, 14:15-15:15
• 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 non-trivial 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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