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
Datum:2013
Hauptverfasser: Farsi, C., Seaton, C., Herbig, H.-C
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2013
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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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-149236
record_format dspace
spelling 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.
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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.
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.
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AT seatonc onorbifoldcriteriaforsymplectictoricquotients
AT herbighc onorbifoldcriteriaforsymplectictoricquotients
first_indexed 2025-12-07T17:00:19Z
last_indexed 2025-12-07T17:00:19Z
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