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CATEGORIES:Algebraic Geometry Seminar
SUMMARY:Okounkov bodies\, moment maps and geodesics of Kah
ler metrics - Julius Ross (Cambridge)
DTSTART;TZID=Europe/London:20111130T141500
DTEND;TZID=Europe/London:20111130T151500
UID:TALK34085AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/34085
DESCRIPTION:The Okounkov body can be thought of as an generali
sation of the\npolytope associated to a projective
toric variety. Starting with a line\nbundle L on
an n-dimensional variety X and a flag of smooth s
ubvarieties\nin X\, the Okounkov body is a convex
subset Delta in R^n\, whose volume\n(with respect
to the Lebesgue measure) is the volume of X (with
respect to\nthe line bundle L). This property for
ms the basis of work by\nLazarsfeld-Mustata who us
e Okounkov bodies to study the volume functional\n
on the space of big divisors.\n\nIn this talk I wi
ll start with a general discussion of Okounkov bod
ies\,\nalong with some examples. I shall then des
cribe ongoing (and very\nunfinished) work with Dav
id Witt-Nystrom which attempts to construct a\nver
sion of the moment map in this setting.
LOCATION:MR13\, CMS
CONTACT:Burt Totaro
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