Nonrational Symplectic Toric Reduction

TL;DR

This paper extends symplectic reduction to nonrational toric geometry, generalizing the process to include non-closed Lie subgroups in the rational case, thus broadening the scope of symplectic reduction techniques.

Contribution

It introduces a novel framework for symplectic reduction within nonrational toric geometry, unifying rational and nonrational cases under a common approach.

Findings

Extended symplectic reduction to nonrational toric geometry.

Generalized reduction for non-closed Lie subgroups in the rational case.

Provided a unified framework connecting rational and nonrational symplectic reductions.

Abstract

In this article, we introduce symplectic reduction in the framework of nonrational toric geometry. When we specialize to the rational case, we get symplectic reduction for the action of a general, not necessarily closed, Lie subgroup of the torus.