Mini-workshop: New developments in Newton-Okounkov bodies. Abstracts from the mini-workshop held August 21--27, 2011.
type: Item
instance of: scholarly article
title: Mini-workshop: New developments in Newton-Okounkov bodies. Abstracts from the mini-workshop held August 21--27, 2011.
zbMATH Open document ID: 1349.00182
DOI: 10.4171/OWR/2011/41
published in: Oberwolfach Reports
publication date: 2016-11-24T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 00B05
Mathematics Subject Classification ID: 00B25
Mathematics Subject Classification ID: 14-06
Mathematics Subject Classification ID: 52-06
Mathematics Subject Classification ID: 14M25
Mathematics Subject Classification ID: 52B12
zbMATH DE Number: 6655972
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/owr/2011/41
OpenAlex ID: W2051439184
description: scientific article; zbMATH DE number 6655972