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CATEGORIES:Algebraic Geometry Seminar
SUMMARY:A geometric characterization of toric varieties -
Roberto Svaldi (Cambridge)
DTSTART;TZID=Europe/London:20151111T141500
DTEND;TZID=Europe/London:20151111T151500
UID:TALK60455AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/60455
DESCRIPTION:Given a pair (X\, D)\, where X is a projective var
iety and D a divisor with mild singularities\, it
is natural to ask how to bound the number of compo
nents 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 an
d show that if the bound is achieved\, or the numb
er of components is close enough to said sum\, the
n 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
CONTACT:Caucher Birkar
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