Poisson resolutions

2004/03/24 by Baohua Fu, Fu, Baohua · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0403408

some changes in section 5

arxiv created 2004/04/05 · arxiv updated 2009/12/01

Abstract

A resolution Z → 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] → S⁽ⁿ⁾ is a Poisson resolution. Furthermore, if Bs|-K_S| = ∅, we prove that this is the unique projective Poisson resolution for S⁽ⁿ⁾.

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