On Orbifold Criteria for Symplectic Toric Quotients

Symmetry Integrability and Geometry-Methods and Applications

article

Carla Farsi¹  Hans-Christian Herbig²  Christopher Seaton³ 

[1] Department of Mathematics, University of Colorado at Boulder, Campus Box 395;Centre for Quantum Geometry of Moduli Spaces;Department of Mathematics and Computer Science, Rhodes College

关键词: singular symplectic reduction;    invariant theory;    orbifold;   

DOI  :  10.3842/SIGMA.2013.032

来源: National Academy of Science of Ukraine

【 摘 要 】

We introduce the notion of regular symplectomorphism and graded regular symplectomorphism between singular phase spaces. Our main concern is to exhibit examples of unitary torus representations whose symplectic quotients cannot be graded regularly symplectomorphic to the quotient of a symplectic representation of a finite group, while the corresponding GIT quotients are smooth. Additionally, we relate the question of simplicialness of a torus representation to Gaussian elimination.

【 授权许可】

Unknown