ℚ-Gorenstein deformations of nonnormal surfaces

Abstract

Let $\Delta \subset H$ be the germ of a nonnormal surface along a proper curve with smooth components such that the high index points of $H$ are semi-log-terminal and the Gorenstein singular points are semi-log-canonical of embedding dimension at most 4. We describe the sheaf $T^1_{qG}(H)$ of ${\Bbb Q}$-Gorenstein deformations of $H$ and we obtain criteria for $\Delta\subset H$ to have ${\Bbb Q}$-Gorenstein terminal smoothings.