Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network

  Advanced Search  

Fields Institute Communications Volume 00, 0000

Summary: Fields Institute Communications
Volume 00, 0000
Kahler geometry of toric manifolds in symplectic coordinates
Miguel Abreu
Departamento de Matematica
Instituto Superior Tecnico
1049-001 Lisboa, Portugal
Abstract. A theorem of Delzant states that any symplectic manifold
(M; !) of dimension 2n, equipped with an e ective Hamiltonian action
of the standard n-torus T n = R n =2Z n , is a smooth projective toric va-
riety completely determined (as a Hamiltonian T n -space) by the image
of the moment map  : M ! R n , a convex polytope P = (M)  R n .
In this paper we show, using symplectic (action-angle) coordinates on
P T n , how all !-compatible toric complex structures on M can be ef-
fectively parametrized by smooth functions on P . We also discuss some
topics suited for application of this symplectic coordinates approach to
Kahler toric geometry, namely: explicit construction of extremal Kahler
metrics, spectral properties of toric manifolds and combinatorics of poly-


Source: Abreu, Miguel - Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa


Collections: Mathematics