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Envelopes of positive metrics with prescribed singularities

Published version
Peer-reviewed

Type

Article

Change log

Authors

Ross, Julius 
Nyström, David Witt 

Abstract

We investigate envelopes of positive metrics with a prescribed singularity type. First we generalise work of Berman to this setting, proving C1,1 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.

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Keywords

Journal Title

Annales de la Faculté des Sciences de Toulouse

Conference Name

Journal ISSN

0240-2963
2258-7519

Volume Title

Publisher

Université Paul Sabatier, Toulouse
Sponsorship
During this project the first author has been supported by a Marie Curie Grant within the 7th European Community Framework Programme and by an EPSRC Career Acceleration Fellowship.