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SUMMARY:A geometric characterization of toric varieties - Roberto Svaldi (
 Cambridge)
DTSTART:20151111T141500Z
DTEND:20151111T151500Z
UID:TALK60455@talks.cam.ac.uk
CONTACT:Caucher Birkar
DESCRIPTION:Given a pair (X\, D)\, where X is a projective variety and D a
  divisor with mild singularities\, it is natural to ask how to bound the n
 umber of components of D. In general such bound does not exist. But when -
 (K_X+D) is positive\, i.e. ample (or nef)\, then a conjecture of Shokurov 
 says this bound should coincide with the sum of the dimension of X and its
  Picard number. We prove the conjecture and show that if the bound is achi
 eved\, or the number of components is close enough to said sum\, then X is
  a toric variety and D is close to being the toric invariant divisor. This
  is joint work with M. Brown\, J. McKernan\, R. Zong.\n
LOCATION:CMS MR13
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