Kahler geometry of toric manifolds in symplectic coordinates
| dc.creator | Abreu, Miguel | |
| dc.date | 2000-04-19 | |
| dc.date.accessioned | 2026-07-07T04:34:48Z | |
| dc.date.available | 2026-07-07T04:34:48Z | |
| dc.description | A theorem of Delzant states that any symplectic manifold $(M,\om)$ of dimension $2n$, equipped with an effective Hamiltonian action of the standard $n$-torus $\T^n = \R^{n}/2π\Z^n$, is a smooth projective toric variety completely determined (as a Hamiltonian $\T^n$-space) by the image of the moment map $ϕ:M\to\R^n$, a convex polytope $P=ϕ(M)\subset\R^n$. In this paper we show, using symplectic (action-angle) coordinates on $P\times \T^n$, how all $\om$-compatible toric complex structures on $M$ can be effectively parametrized by smooth functions on $P$. We also discuss some topics suited for application of this symplectic coordinates approach to Kähler toric geometry, namely: explicit construction of extremal Kähler metrics, spectral properties of toric manifolds and combinatorics of polytopes. | |
| dc.description | 24 pages, to appear in "Toric Varieties in Algebraic Geometry and Physics", V. Batyrev (ed.), AMS | |
| dc.identifier | https://arxiv.org/abs/math/0004122 | |
| dc.identifier | http://arxiv.org/abs/math/0004122 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59046 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Primary 53C55; Secondary 14M25, 58F05 | |
| dc.title | Kahler geometry of toric manifolds in symplectic coordinates | |
| dc.type | text |