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Analytic test configurations and geodesic rays

Journal article
Authors J. Ross
David Witt Nyström
Published in The Journal of Symplectic Geometry
Volume 12
Issue 1
Pages 125-169
ISSN 1527-5256
Publisher International Press of Boston, Inc.
Publication year 2014
Published at Department of Mathematical Sciences
Pages 125-169
Language en
Links dx.doi.org/10.4310/JSG.2014.v12.n1....
Subject categories Mathematics

Abstract

Starting with the data of a curve of singularity types, we use the Legendre transform to construct weak geodesic rays in the space of locally bounded metrics on an ample line bundle L over a compact manifold. Using this we associate weak geodesics to suitable filtrations of the algebra of sections of L. In particular this works for the natural filtration coming from an algebraic test configuration, and we show how this recovers the weak geodesic ray of Phong-Sturm.

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