On asymptotics for the Mabuchi energy functional
| dc.creator | Phong, D. H. | |
| dc.creator | Sturm, Jacob | |
| dc.date | 2003-12-31 | |
| dc.date.accessioned | 2026-07-07T05:04:19Z | |
| dc.date.available | 2026-07-07T05:04:19Z | |
| dc.description | If $M$ is a projective manifold in $P^N$, then one can associate to each one parameter subgroup $H$ of $SL(N+1)$ the Mumford $μ$ invariant. The manifold $M$ is Chow-Mumford stable if $μ$ is positive for all $H$. Tian has defined the notion of K-stability, and has shown it to be intimately related to the existence of Kähler-Einstein metrics. The manifold $M$ is K-stable if $μ'$ is positive for all $H$, where $μ'$ is an invariant which is defined in terms of the Mabuchi K-energy. In this paper we derive an explicit formula for $μ'$ in the case where $M$ is a curve. The formula is similar to Mumford's formula for $μ$, and is likewise expressed in terms of the vertices of the Newton diagram of a basis of holomorphic sections for the hyperplane line bundle. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0312528 | |
| dc.identifier | http://arxiv.org/abs/math/0312528 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69758 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.title | On asymptotics for the Mabuchi energy functional | |
| dc.type | text |