Straight Equisingular Deformations and Punctual Hilbert Schemes
Abstract
We study "straight equisingular deformations", a linear subfunctor of all equisingular deformations and describe their seminuniversal deformation by an ideal containing the fixed Tjurina ideal. Moreover, we show that the base space of the seminuniversal straight equisingular deformation appears as the fibre of a morphism from the {\mu}-constant stratum onto a punctual Hilbert scheme parametrizing certain zero-dimensional schemes concentrated in the singular point. Although equisingular deformations of plane curve singularities are very well understood, we believe that this aspect may give a new insight in their inner structure.
Cite
@article{arxiv.1810.06444,
title = {Straight Equisingular Deformations and Punctual Hilbert Schemes},
author = {Gert-Martin Greuel},
journal= {arXiv preprint arXiv:1810.06444},
year = {2019}
}
Comments
Dedicated to L\^e D\~ung Tr\'ang on the occasion of his 70th Birthday. Minor changes in v2. To appear in "Contemporary Mathematics"