We study deformations of nonsingular Poisson varieties and Poisson invertible sheaves, which extend the flat deformation theory of nonsingular varieties and invertible sheaves. In the Appendix, we study deformations of Poisson vector bundles. We identify first-order deformations and obstructions.
"Deformations of nonsingular Poisson varieties and Poisson invertible sheaves." Kyoto J. Math. 60 (2) 511 - 541, June 2020. https://doi.org/10.1215/21562261-2019-0042