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- W2022126883 abstract "Let $X$ be a compact complex manifold, $Lto X$ an ample line bundle over $X$, and ${cal H}$ the space of all positively curved metrics on $L$. We show that a pair $(h_0,T)$ consisting of a point $h_0in {cal H}$ and a test configuration $T=({cal L}to {cal X}to {bf C})$, canonically determines a weak geodesic ray $R(h_0,T)$ in ${cal H}$ which emanates from $h_0$. Thus a test configuration behaves like a vector field on the space of Kahler potentials ${cal H}$. We prove that $R$ is non-trivial if the ${bf C}^times$ action on $X_0$, the central fiber of $cal X$, is non-trivial. The ray $R$ is obtained as limit of smooth geodesic rays $R_ksubset{cal H}_k$, where ${cal H}_ksubset{cal H}$ is the subspace of Bergman metrics." @default.
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- W2022126883 date "2007-01-01" @default.
- W2022126883 modified "2023-10-11" @default.
- W2022126883 title "Test configurations for K-stability and geodesic rays" @default.
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- W2022126883 doi "https://doi.org/10.4310/jsg.2007.v5.n2.a3" @default.
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