From formal smoothings to geometric smoothings
Algebraic Geometry
2023-02-15 v2
Abstract
Let X be a projective, equidimensional, singular scheme over an algebraically closed field. Then the existence of a geometric smoothing (i.e. a family of deformations of X over a smooth base curve whose generic fibre is smooth) implies the existence of a formal smoothing as defined by Tziolas. In this paper we address the reverse question giving sufficient conditions on X that guarantee the converse, i.e. formal smoothability implies geometric smoothability. This is useful in light of Tziolas' results giving sufficient criteria for the existence of formal smoothings.
Keywords
Cite
@article{arxiv.2211.14089,
title = {From formal smoothings to geometric smoothings},
author = {Alessandro Nobile},
journal= {arXiv preprint arXiv:2211.14089},
year = {2023}
}