Q-Gorenstein deformations of non-normal surfaces

TL;DR

This paper explores the deformation theory of non-normal surfaces, providing an example of a stable surface that is locally smoothable but lacks a global smoothing, highlighting complexities in surface deformation.

Contribution

It introduces a specific example demonstrating the limitations of smoothing non-normal surfaces globally, advancing understanding of surface deformation theory.

Findings

Presented an example of a stable surface with local but not global smoothability

Highlighted the distinction between local and global smoothing in surface deformations

Contributed to the classification of non-normal surface deformations

Abstract

Revised Version. An example of a locally smoothable stable surface that does not have a global smoothing has been added.