Analytic test configurations and geodesic rays

2011/01/08 by Ross, Julius, Nystrom, David Witt · 4 citations
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1101.1612

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

Cited by

• Quantization for Semipositive Adjoint Line Bundles
• Monge-Ampère equations with prescribed singularities on compact Hermitian manifolds
• A YTD correspondence for constant scalar curvature metrics
• Lines in the space of Kähler metrics

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