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Galois closures and elementary components of Hilbert schemes of points.
- Source :
-
Selecta Mathematica, New Series . Apr2024, Vol. 30 Issue 2, p1-35. 35p. - Publication Year :
- 2024
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *NUCLEAR families
*ALGEBRA
Subjects
Details
- Language :
- English
- ISSN :
- 10221824
- Volume :
- 30
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Selecta Mathematica, New Series
- Publication Type :
- Academic Journal
- Accession number :
- 175966267
- Full Text :
- https://doi.org/10.1007/s00029-024-00915-9