Analytic test configurations and geodesic rays

Details Analytic test configurations and geodesic rays Analytic test configurations and geodesic rays

2011-01-08

arxiv.org/abs/1101.1612v2

Mathematics

Algebraic Geometry

42 pages. Version 2 fixes Theorem 7.9

Scientific paper

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 in this case we recover the weak geodesic ray of Phong-Sturm.

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