2003/02/27 by D. Burns, Victor Guillemin, V. Guillemin +2
Mathematics · #53D20 (Primary) 53C55 (Secondary) #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:53C55 #msc:53D20
paper · pdf · doi:10.48550/arxiv.math/0302350
20 pp., no figures. Submitted, Comm. An. and Geom
arxiv created 2003/02/27 · openalex publication_date 2003/02/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a Kaehler manifold with a free, holomorphic and Hamiltonian action of the standard n-torus T. We give a simple, explicit and canonical formula for the Kaehler potential on the Kaehler reduction of M. As a consequence we can derive improvements of several classical results known for more general Hamiltonian reductions. Among these are a forms-level proof of the Duistermaat-Heckman theorem; an elementary proof of Atiyah's proof of the convexity of the moment image of a complexified T-orbit; another formula due to Biquard-Gauduchon for the Kaehler potential; and a formula in terms of moment data for the Kaehler metric on a toric variety, due originally to the second author.