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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Semifree symplectic circle actions on $4$-orbifolds

Author: L. Godinho
Journal: Trans. Amer. Math. Soc. 358 (2006), 4919-4933
MSC (2000): Primary 53D20
Published electronically: April 11, 2006
MathSciNet review: 2231878
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Abstract: A theorem of Tolman and Weitsman states that all symplectic semifree circle actions with isolated fixed points on compact symplectic manifolds must be Hamiltonian and have the same equivariant cohomology and Chern classes of $(\mathbb {C}P^1)^n$ equipped with the standard diagonal circle action. In this paper, we show that the situation is much different when we consider compact symplectic orbifolds. Focusing on $4$-orbifolds with isolated cone singularities, we show that such actions, besides being Hamiltonian, can now be obtained from either $S^2\times S^2$ or a weighted projective space, or a quotient of one of these spaces by a finite cyclic group, by a sequence of special weighted blow-ups at fixed points. In particular, they can have any number of fixed points.

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Additional Information

L. Godinho
Affiliation: Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
MR Author ID: 684216
ORCID: 0000-0002-6329-3002

Received by editor(s): September 21, 2004
Published electronically: April 11, 2006
Additional Notes: This research was partially supported by FCT through program POCTI/FEDER and grant POCTI/MAT/57888/2004, and by Fundação Calouste Gulbenkian
Article copyright: © Copyright 2006 American Mathematical Society