On Orbifold Criteria for Symplectic Toric Quotients
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 rep...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2013 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2013
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149236 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Farsi, C. Seaton, C. Herbig, H.-C 2019-02-19T19:06:21Z 2019-02-19T19:06:21Z 2013 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. 1815-0659 2010 Mathematics Subject Classification: 53D20; 58A40; 13A50; 14L24; 57R18 DOI: http://dx.doi.org/10.3842/SIGMA.2013.032 https://nasplib.isofts.kiev.ua/handle/123456789/149236 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Orbifold Criteria for Symplectic Toric Quotients Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On Orbifold Criteria for Symplectic Toric Quotients |
| spellingShingle |
On Orbifold Criteria for Symplectic Toric Quotients Farsi, C. Seaton, C. Herbig, H.-C |
| title_short |
On Orbifold Criteria for Symplectic Toric Quotients |
| title_full |
On Orbifold Criteria for Symplectic Toric Quotients |
| title_fullStr |
On Orbifold Criteria for Symplectic Toric Quotients |
| title_full_unstemmed |
On Orbifold Criteria for Symplectic Toric Quotients |
| title_sort |
on orbifold criteria for symplectic toric quotients |
| author |
Farsi, C. Seaton, C. Herbig, H.-C |
| author_facet |
Farsi, C. Seaton, C. Herbig, H.-C |
| publishDate |
2013 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149236 |
| citation_txt |
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. |
| work_keys_str_mv |
AT farsic onorbifoldcriteriaforsymplectictoricquotients AT seatonc onorbifoldcriteriaforsymplectictoricquotients AT herbighc onorbifoldcriteriaforsymplectictoricquotients |
| first_indexed |
2025-12-07T17:00:19Z |
| last_indexed |
2025-12-07T17:00:19Z |
| _version_ |
1850869619661733888 |