Singular Reduction of Generalized Complex Manifolds

In this paper, we develop results in the direction of an analogue of Sjamaar and Lerman's singular reduction of Hamiltonian symplectic manifolds in the context of reduction of Hamiltonian generalized complex manifolds (in the sense of Lin and Tolman). Specifically, we prove that if a compact Li...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2010
Автор: Goldberg, T.E.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2010
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/146509
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Singular Reduction of Generalized Complex Manifolds / T.E. Goldberg // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 20 назв. — англ.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-146509
record_format dspace
spelling Goldberg, T.E.
2019-02-09T19:37:49Z
2019-02-09T19:37:49Z
2010
Singular Reduction of Generalized Complex Manifolds / T.E. Goldberg // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 20 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 53D20; 53D18; 53C15
DOI:10.3842/SIGMA.2010.081
https://nasplib.isofts.kiev.ua/handle/123456789/146509
In this paper, we develop results in the direction of an analogue of Sjamaar and Lerman's singular reduction of Hamiltonian symplectic manifolds in the context of reduction of Hamiltonian generalized complex manifolds (in the sense of Lin and Tolman). Specifically, we prove that if a compact Lie group acts on a generalized complex manifold in a Hamiltonian fashion, then the partition of the global quotient by orbit types induces a partition of the Lin-Tolman quotient into generalized complex manifolds. This result holds also for the reduction of Hamiltonian generalized Kähler manifolds.
The author would like to thank Reyer Sjamaar for his help in understanding the singular reduction in the symplectic case, Yi Lin for several extremely helpful conversations, Tomoo Matsumura for introducing him to generalized complex geometry, the referees for many useful suggestions, and his family and friends for their unwavering support.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Singular Reduction of Generalized Complex Manifolds
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Singular Reduction of Generalized Complex Manifolds
spellingShingle Singular Reduction of Generalized Complex Manifolds
Goldberg, T.E.
title_short Singular Reduction of Generalized Complex Manifolds
title_full Singular Reduction of Generalized Complex Manifolds
title_fullStr Singular Reduction of Generalized Complex Manifolds
title_full_unstemmed Singular Reduction of Generalized Complex Manifolds
title_sort singular reduction of generalized complex manifolds
author Goldberg, T.E.
author_facet Goldberg, T.E.
publishDate 2010
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description In this paper, we develop results in the direction of an analogue of Sjamaar and Lerman's singular reduction of Hamiltonian symplectic manifolds in the context of reduction of Hamiltonian generalized complex manifolds (in the sense of Lin and Tolman). Specifically, we prove that if a compact Lie group acts on a generalized complex manifold in a Hamiltonian fashion, then the partition of the global quotient by orbit types induces a partition of the Lin-Tolman quotient into generalized complex manifolds. This result holds also for the reduction of Hamiltonian generalized Kähler manifolds.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/146509
citation_txt Singular Reduction of Generalized Complex Manifolds / T.E. Goldberg // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 20 назв. — англ.
work_keys_str_mv AT goldbergte singularreductionofgeneralizedcomplexmanifolds
first_indexed 2025-12-07T17:42:28Z
last_indexed 2025-12-07T17:42:28Z
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