Author： Godinho L.
Publisher： Springer Publishing Company
ISSN： 0232-704X
Source： Annals of Global Analysis and Geometry, Vol.20, Iss.2, 2001-09, pp. : 117-162
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Abstract
In the first part of this paper we study different blow-up constructions on symplectic orbifolds. Unlike the manifold case, we can define different blow-ups by using different circle actions. In the second part, we use some of these constructions to describe the behavior of reduced spaces of a Hamiltonian circle action on a symplectic orbifold, when passing a critical level of its Hamiltonian function. Using these descriptions, we generalize, in the manifold case, the wall-crossing theorem of Guillemin and Sternberg to the case of a Hamiltonian torus action not necessarily quasi-free and also the Duistermaat–Heckman theorem to intervals of values of the Hamiltonian function containing critical values.
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