Grassmannians and Singularities

Abstract

Let $X$ be an integral scheme of finite presentation over a perfect field. Let $q$ be a singular closed point of $X$. We prove that there exists an open subset $V$ of $X$ containing $q$ such that $V$ admits a resolution, that is, there exists a smooth scheme $\widetilde V$ and a proper birational morphism from $\widetilde V$ onto $V$.