## Journal of Symplectic Geometry

### Analytic test configurations and geodesic rays

#### 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.

#### Article information

Source
J. Symplectic Geom., Volume 12, Number 1 (2014), 125-169.

Dates
First available in Project Euclid: 29 August 2014