Okounkov bodies, moment maps and geodesics of Kahler metrics

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• Julius Ross (Cambridge)
• Wednesday 30 November 2011, 14:15-15:15
• MR13, CMS.

If you have a question about this talk, please contact Burt Totaro.

The Okounkov body can be thought of as an generalisation of the polytope associated to a projective toric variety. Starting with a line bundle L on an n-dimensional variety X and a flag of smooth subvarieties in X, the Okounkov body is a convex subset Delta in R^n, whose volume (with respect to the Lebesgue measure) is the volume of X (with respect to the line bundle L). This property forms the basis of work by Lazarsfeld-Mustata who use Okounkov bodies to study the volume functional on the space of big divisors.

In this talk I will start with a general discussion of Okounkov bodies, along with some examples. I shall then describe ongoing (and very unfinished) work with David Witt-Nystrom which attempts to construct a version of the moment map in this setting.

This talk is part of the Algebraic Geometry Seminar series.

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