Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 9 (2013), 032, 33 pages      arXiv:1205.1870      https://doi.org/10.3842/SIGMA.2013.032

On Orbifold Criteria for Symplectic Toric Quotients

Carla Farsi a, Hans-Christian Herbig b and Christopher Seaton c
a) Department of Mathematics, University of Colorado at Boulder, Campus Box 395, Boulder, CO 80309-0395, USA
b) Centre for Quantum Geometry of Moduli Spaces, Ny Munkegade 118 Building 1530, 8000 Aarhus C, Denmark
c) Department of Mathematics and Computer Science, Rhodes College, 2000 N. Parkway, Memphis, TN 38112, USA

Received August 07, 2012, in final form April 02, 2013; Published online April 12, 2013

Abstract
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.

Key words: singular symplectic reduction; invariant theory; orbifold.

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