Test Configurations for K-Stability and Geodesic Rays
| dc.creator | Phong, D. H. | |
| dc.creator | Sturm, Jacob | |
| dc.date | 2006-06-17 | |
| dc.date | 2006-06-30 | |
| dc.date.accessioned | 2026-07-07T07:17:24Z | |
| dc.date.available | 2026-07-07T07:17:24Z | |
| dc.description | Let $X$ be a compact complex manifold, $L\to X$ 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 $h_0\in {\cal H}$ 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 Kähler 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 $R_k\subset{\cal H}_k$, where ${\cal H}_k\subset{\cal H}$ is the subspace of Bergman metrics. | |
| dc.description | 27 pages, no figure; references added; typos corrected | |
| dc.identifier | https://arxiv.org/abs/math/0606423 | |
| dc.identifier | http://arxiv.org/abs/math/0606423 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/113929 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.title | Test Configurations for K-Stability and Geodesic Rays | |
| dc.type | text |