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. © 2015 The Author(s).