New elementary components of the Gorenstein locus of the Hilbert scheme of points
Robert Szafarczyk
TL;DR
This paper constructs explicit examples of nonsmoothable Gorenstein algebras with specific Hilbert functions, establishing a new infinite family of elementary components in the Gorenstein locus of the Hilbert scheme of points and resolving the cubic case of Iarrobino's conjecture.
Contribution
It introduces a new infinite family of elementary components in the Gorenstein locus and solves the cubic case of Iarrobino's conjecture.
Findings
Constructed explicit nonsmoothable Gorenstein algebras with Hilbert function (1,n,n,1)
Established a new infinite family of elementary components in the Gorenstein locus
Solved the cubic case of Iarrobino's conjecture
Abstract
We construct new explicit examples of nonsmoothable Gorenstein algebras with Hilbert function . This gives a new infinite family of elementary components in the Gorenstein locus of the Hilbert scheme of points and solves the cubic case of Iarrobino's conjecture.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Polynomial and algebraic computation