Every symplectic toric orbifold is a centered reduction of a Cartesian product of weighted projective spaces

Abstract

We prove that every symplectic toric orbifold is a centered reduction of a Cartesian product of weighted projective spaces. A theorem of Abreu and Macarini shows that if the level set of the reduction passes through a non-displaceable set then the image of this set in the reduced space is also non-displaceable. Using this result we show that every symplectic toric orbifold contains a non-displaceable fiber and we identify this fiber.

arXiv comment20 pages, 11 figures; Final version. Accepted at IMRN. Comments from the referees included. Section about Gromov width added. Moreover we fixed some small mistakes that unfortunately made it to the published version (moment polytope for the weighted projective space was not fully correct; at some point a not connected subgroup was called a torus)