2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74189We 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.AmSLaTeX, 18 pages, 11 bibliography items; minor corrections madeAlgebraic GeometrySymplectic Geometry14L30 (Primary) 53D05, 53D20 (Secondary)text