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On the coordinate ring of a projective Poisson scheme

D. Kaledin
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Abstract

The 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.

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D. Kaledin. 2005-04-27. On the coordinate ring of a projective Poisson scheme. https://arxiv.org/abs/math/0312134

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