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Envelopes of positive metrics with prescribed singularities

dc.creatorRoss, Julius
dc.creatorNyström, David Witt
dc.date.accessioned2016-07-14
dc.date.accessioned2018-11-24T23:26:51Z
dc.date.available2016-08-31T12:58:58Z
dc.date.available2018-11-24T23:26:51Z
dc.date.issued2016
dc.identifierhttps://www.repository.cam.ac.uk/handle/1810/257497
dc.identifier.urihttp://repository.aust.edu.ng/xmlui/handle/123456789/3899
dc.description.abstractWe investigate envelopes of positive metrics with a prescribed singularity type. First we generalise work of Berman to this setting, proving C$^{1,1}$ regularity of such envelopes, showing their Monge-Ampère measure is supported on a certain “equilibrium set” and connecting with the asymptotics of the partial Bergman functions coming from multiplier ideals. We investigate how these envelopes behave on certain products, and how they relate to the Legendre transform of a test curve of singularity types in the context of geodesic rays in the space of Kähler potentials. Finally we consider the associated exhaustion function of these equilibrium sets, connecting it both to the Legendre transform and to the geometry of the Okounkov body.
dc.languageen
dc.publisherUniversité Paul Sabatier, Toulouse
dc.publisherAnnales de la Faculté des Sciences de Toulouse
dc.titleEnvelopes of positive metrics with prescribed singularities
dc.typeArticle


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