2 problems

Let $X$ be a singularity over a field of characteristic zero, and let its tangent sheaf be free. Lipman–Zariski conjecture. The singularity $X$ is smooth. This conjecture asks whet…

Let $Y$ be an analytic variety, and let $T_Y:=\operatorname{Hom}(\Omega_Y^1,\mathcal{O}_Y)$ be its tangent sheaf, where $\Omega_Y^1$ is the sheaf of Kähler differentials. Zariski–L…