Let $X$ be a compact complex manifold with structure sheaf $\mathscr{O}_X$ (the sheaf of holomorphic functions on $X$). 

>What is the geometric meaning (if any) of $H^2(X, \mathscr{O}_X)$?


In the [comments](https://mathoverflow.net/questions/412512/what-is-the-geometric-meaning-of-h2x-mathscro-x#comment1057131_412512), Piotr Achinger mentions that $H^2(X, \mathscr{O}_X)$ is the tangent space of the (formal) Brauer group. Let me ask a follow up question: 

>What is the geometric meaning (if any) of $H^2(X, \mathscr{O}_X)$ if the Brauer group, and the cohomological Brauer group are both trivial?