Poisson resolutions

Details Poisson resolutions Poisson resolutions

2004-03-24

arxiv.org/abs/math/0403408v2

Mathematics

Algebraic Geometry

some changes in section 5

Scientific paper

A resolution $Z \to X$ of a Poisson variety $X$ is called {\em Poisson} if every Poisson structure on $X$ lifts to a Poisson structure on $Z$. For symplectic varieties, we prove that Poisson resolutions coincide with symplectic resolutions. It is shown that for a Poisson surface $S$, the natural resolution $S^{[n]} \to S^{(n)}$ is a Poisson resolution. Furthermore, if $Bs|-K_S| = \emptyset$, we prove that this is the unique projective Poisson resolution for $S^{(n)}$.

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