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On Orbifold Criteria for Symplectic Toric Quotients
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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On Orbifold Criteria for Symplectic Toric Quotients
Інший ID:
2010 Mathematics Subject Classification: 53D20; 58A40; 13A50; 14L24; 57R18
DOI: http://dx.doi.org/10.3842/SIGMA.2013.032
DOI: http://dx.doi.org/10.3842/SIGMA.2013.032
Посилання:
On Orbifold Criteria for Symplectic Toric Quotients / C. Farsi, H-C. Herbig, C. Seaton // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 31 назв. — англ.
Підтримка:
The authors would like to thank Srikanth Iyengar, Luchezar Avramov, Markus Pflaum, Johan Martens, Karl-Heinz Fieseler, Jedrzej Sniatycki, Gerry Schwarz, Johannes Huebschmann,
Michael J. Field and Graeme Wilkin for promptly answering questions, stimulating discussions,
and moral support. We would also like to thank the referees for helpful suggestions and comments.
C.F. would like to thank the University of Florence for hospitality during the completion of
this manuscript. The research of H.-C. H. has been supported by the Center for the Quantum
Geometry of Moduli spaces which is funded by the Danish National Research Foundation, and
by the Department of Mathematics of the University of Nebraska at Lincoln. C.S. received
support from the Center for the Quantum Geometry of Moduli spaces, a Rhodes College Faculty
Development Endowment Grant, and a grant to Rhodes College from the Andrew W. Mellon
Foundation.
Дата:
2013
Переглядів:
582
Завантажень:
240
Анотація:
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.
