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In this paper, we study deformations of nonsingular Poisson varieties,deformations of Poisson invertible sheaves and simultaneous deformations ofnonsingular Poisson varieties and Poisson invertible sheaves, which extend flatdeformation theory of nonsingular varieties and invertible sheaves. In anappendix, we study deformations of Poisson vector bundles. We identifyfirst-order deformations and obstructions.

Deformations of nonsingular Poisson varieties and Poisson invertible sheaves