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Let $X$ be an (affine) Poisson variety (not necessarily smooth) over an algebraically closed field of characteristic 0 (such as $\mathbb{C}$), denote $\mathcal{O}(X)$ its ring of functions and $\{-,-\}...

In context of Abelian varieties there are a couple of equivalent ways to introduce the polarization of a algebraic variety. One way is to choose a line bundle $\mathcal{L}$ which satisfies certain ...

Let $X$ be a complex algebraic variety and let $D$ denote any $\mathbb C[[h]]$-deformation of $\mathcal O_X$. Suppose that $D$ is trivial. Then it is well-known that obstructions to deforming any $X$-...