Galois closures and elementary components of Hilbert schemes of points
Algebraic Geometry
2023-12-18 v2 Commutative Algebra
Number Theory
Abstract
Bhargava and the first-named author of this paper introduced a functorial Galois closure operation for finite-rank ring extensions, generalizing constructions of Grothendieck and Katz--Mazur. In this paper, we generalize Galois closures and apply them to construct a new infinite family of irreducible components of Hilbert schemes of points. We show that these components are elementary, in the sense that they parametrize algebras supported at a point. Furthermore, we produce secondary families of elementary components obtained from Galois closures by modding out by suitable socle elements.
Keywords
Cite
@article{arxiv.2210.14310,
title = {Galois closures and elementary components of Hilbert schemes of points},
author = {Matthew Satriano and Andrew P. Staal},
journal= {arXiv preprint arXiv:2210.14310},
year = {2023}
}