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arXiv · 0712.3599

Test configurations, large deviations and geodesic rays on toric varieties

Jian Song·Steve Zelditch
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Abstract

This article contains a detailed study, in the toric case, of the test configuration geodesic rays defined by Phong-Sturm. We show that the `Bergman approximations' of Phong-Sturm converge in C^1 to the geodesic ray and that the geodesic ray itself is C^{1,1} and no better. The \kahler metrics associated to the geodesic ray of potentials are discontinuous across certain hypersurfaces and are degenerate on certain open sets. A novelty in the analysis is the connection between Bergman metrics, Bergman kernels and the theory of large deviations.

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Jian Song, Steve Zelditch. 2007-12-21. Test configurations, large deviations and geodesic rays on toric varieties. https://arxiv.org/abs/0712.3599

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