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Singular Reduction of Generalized Complex Manifolds
Репозиторій DSpace/Manakin
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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Singular Reduction of Generalized Complex Manifolds
Інший ID:
2010 Mathematics Subject Classification: 53D20; 53D18; 53C15
DOI:10.3842/SIGMA.2010.081
DOI:10.3842/SIGMA.2010.081
Посилання:
Singular Reduction of Generalized Complex Manifolds / T.E. Goldberg // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 20 назв. — англ.
Підтримка:
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.
Дата:
2010
Переглядів:
443
Завантажень:
263
Анотація:
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.
