Kahler geometry of toric manifolds in symplectic coordinates

@article{Abreu2000KahlerGO,
  title={Kahler geometry of toric manifolds in symplectic coordinates},
  author={Miguel Abreu},
  journal={arXiv: Differential Geometry},
  year={2000}
}
  • M. Abreu
  • Published 19 April 2000
  • Mathematics
  • arXiv: Differential Geometry
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 $\T^n = \R^{n}/2\pi\Z^n$, is a smooth projective toric variety completely determined (as a Hamiltonian $\T^n$-space) by the image of the moment map $\phi:M\to\R^n$, a convex polytope $P=\phi(M)\subset\R^n$. In this paper we show, using symplectic (action-angle) coordinates on $P\times \T^n$, how all $\om$-compatible toric complex… 
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