Smoothings of lci proper schemes

TL;DR

This paper establishes criteria for when proper lci schemes and DM stacks can be smoothed geometrically, including applications to polarized K3 surfaces and stable varieties, without requiring the schemes to be reduced.

Contribution

It provides new criteria for the existence of smoothings of proper lci schemes and DM stacks, extending previous results to non-reduced cases and polarized schemes.

Findings

Criteria for smoothability of proper lci schemes and DM stacks.

Application of criteria to polarized K3 surfaces.

Application to stable varieties.

Abstract

We give criteria for the existence of geometric smoothings of a proper lci scheme or a DM stack $X$ as well as for a polarized lci scheme $(X,L)$, without assuming that $X$ is reduced. As applications, we give criteria for the smoothability of polarized K3 surfaces and of stable varieties.