Galois closures and elementary components of Hilbert schemes of points

Matthew Satriano; Andrew P. Staal

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arXiv · 2210.14310

Galois closures and elementary components of Hilbert schemes of points

Matthew Satriano·Andrew P. Staal

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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.

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BibTeX RIS

Matthew Satriano, Andrew P. Staal. 2022-10-25. Galois closures and elementary components of Hilbert schemes of points. https://arxiv.org/abs/2210.14310

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