Smoothings of schemes with non-isolated singularities

TL;DR

This paper investigates the deformation theory of schemes with non-isolated singularities, providing criteria and obstruction spaces for smoothings and Q-Gorenstein smoothings, advancing understanding of their deformation behavior.

Contribution

It introduces explicit criteria and obstruction spaces for smoothings and Q-Gorenstein smoothings of schemes with non-isolated singularities.

Findings

Derived obstruction spaces for deformations

Established criteria for smoothings of schemes

Analyzed conditions for Q-Gorenstein smoothings

Abstract

In this paper we study the deformation and Q-Gorenstein deformation theory of schemes with non-isolated singularities. We obtain obstruction spaces for the existence of deformations and also for local deformations to exist globally. Finally we obtain explicit criteria in order for a pure and reduced scheme of finite type over a field $k$ to have smoothings and Q-Gorenstein smoothings.