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SUMMARY:Anticanonical divisors and curve classes on Fano manifolds - Andre
 as Hoering (Jussieu)
DTSTART:20121017T131500Z
DTEND:20121017T141500Z
UID:TALK39532@talks.cam.ac.uk
CONTACT:Caucher Birkar
DESCRIPTION:Let X be a Fano manifold\, i.e. a projective complex manifold 
 such that -K_X is ample.\nIf X has dimension three a classical but non-tri
 vial result by Shokurov says that a general\nelement in the\nanticanonical
  system |-K_X| is a smooth surface. In higher dimension the situation is m
 uch more\ncomplicated\,\nwe prove that for a fourfold a general anticanoni
 cal divisor has at most isolated singularities.\nAs an application we obta
 in\nan integral version of the Hodge conjecture : for a Fano fourfold the 
 group H^6(X\, Z) is\ngenerated over Z by classes of curves.\nThis is joint
  work with Claire Voisin.\n
LOCATION:MR 13\, CMS
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