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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Semifree symplectic circle actions on $4$-orbifolds
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by L. Godinho PDF
Trans. Amer. Math. Soc. 358 (2006), 4919-4933 Request permission


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
  • Email:
  • 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
  • © Copyright 2006 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 358 (2006), 4919-4933
  • MSC (2000): Primary 53D20
  • DOI:
  • MathSciNet review: 2231878