## Mini-Workshop: New Developments in Newton-Okounov Bodies

 dc.date.accessioned 2019-10-24T14:21:12Z dc.date.available 2019-10-24T14:21:12Z dc.date.issued 2011 dc.identifier.uri http://publications.mfo.de/handle/mfo/3255 dc.description.abstract 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. dc.title Mini-Workshop: New Developments in Newton-Okounov Bodies dc.rights.license Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. de dc.rights.license This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. en dc.identifier.doi 10.14760/OWR-2011-41 local.series.id OWR-2011-41 local.subject.msc 05 local.subject.msc 14 local.sortindex 695 local.date-range 21 Aug - 27 Aug 2011 local.workshopcode 1134b local.workshoptitle Mini-Workshop: New Developments in Newton-Okounov Bodies local.organizers Megumi Harada, Hamilton; Kiumars Kaveh, Pittsburgh; Askold Khovanskii, Toronto local.report-name Workshop Report 2011,41 local.opc-photo-id 1134b local.publishers-doi 10.4171/OWR/2011/41 local.ems-reference 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
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