Equivariant symplectic geometry of cotangent bundles, II

Details Equivariant symplectic geometry of cotangent bundles, II Equivariant symplectic geometry of cotangent bundles, II

2005-02-14

arxiv.org/abs/math/0502284v2

Mathematics

Algebraic Geometry

AmSLaTeX, 18 pages, 11 bibliography items; minor corrections made

Scientific paper

We examine the structure of the cotangent bundle $T^{*}X$ of an algebraic variety $X$ acted on by a reductive group $G$ from the viewpoint of equivariant symplectic geometry. In particular, we construct an equivariant symplectic covering of $T^{*}X$ by the cotangent bundle of a certain variety of horospheres in $X$, and integrate the invariant collective motion on $T^{*}X$. These results are based on a "local structure theorem" describing the action of a certain parabolic in $G$ on an open subset of $X$, which is interesting by itself.

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