Oberwolfach Reports


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Volume 8, Issue 3, 2011, pp. 2327–2363
DOI: 10.4171/OWR/2011/41

Published online: 2012-04-11

Mini-Workshop: New Developments in Newton-Okounkov Bodies

Megumi Harada[1], Kiumars Kaveh[2] and Askold Khovanskii[3]

(1) McMaster University, Hamilton, Canada
(2) University of Pittsburgh, USA
(3) University of Toronto, Toronto, Canada

The theory of Newton-Okounkov bodies, also called Okounkov bodies, is a new connection between algebraic geometry and convex geometry. It generalizes the well-known and extremely rich correspondence between geometry of toric varieties and combinatorics of convex integral polytopes. Okounkov bodies were first introduced by Andrei Okounkov, in a construction motivated by a question of Khovanskii concerning convex bodies govering the multiplicities of representations. Recently, Kaveh-Khovanskii and Lazarsfeld-Mustata have generalized and systematically developed Okounkov’s construction, showing the existence of convex bodies which capture much of the asymptotic information about the geometry of ($X,D$) where $X$ is an algebraic variety and $D$ is a big divisor. The study of Okounkov bodies is a new research area with many open questions. The goal of this mini-workshop was to bring together a core group of algebraic/symplectic geometers currently working on this topic to establish the groundwork for future development of this area.

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Harada Megumi, Kaveh Kiumars, Khovanskii Askold: Mini-Workshop: New Developments in Newton-Okounkov Bodies. Oberwolfach Rep. 8 (2011), 2327-2363. doi: 10.4171/OWR/2011/41