Journal of Symplectic Geometry

Analytic test configurations and geodesic rays

Julius Ross and David Witt Nyström

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

First available in Project Euclid: 29 August 2014

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Ross, Julius; Nyström, David Witt. Analytic test configurations and geodesic rays. J. Symplectic Geom. 12 (2014), no. 1, 125--169.

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