Mathematics

It is important in the theory of moduli spaces of surfaces of general type (and its higher-dimensional analogues) to know when a variety with non-isolated singularity can be geometrically smoothed. Tziolas, in his paper "Smoothing of Schemes with Nonisolated Singularities", gave a useful criterion to deduce formal smoothness. In this talk, we will show how to pass from formal smoothness to geometric smoothness. The talk is divided in two parts: in the first part I'll give an introduction to formal schemes; the second part is devoted to present our result.