2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69492The projective coordinate ring of a projective Poisson scheme $X$ does not usually admit a structure of a Poisson algebra. We show that when $H^1(X,O_X)=H^2(X,O_X)=0$, this can be corrected by embedding $X$ into a canonical one-parameter deformation. The scheme $X$ then becomes the Hamiltonian reduction of the spectrum of the deformed projective coordinate ring with respect to $G_m$. The projection into the base of the deformation is the moment map.Final version, slightly expanded; to appear in MRLAlgebraic Geometrytext