The Hilbert scheme of 11 points in A^3 is irreducible
Theodosios Douvropoulos, Joachim Jelisiejew, Bernt Ivar Utst{\o}l, N{\o}dland, and Zach Teitler
TL;DR
This paper proves that the Hilbert scheme of 11 points in three-dimensional affine space is irreducible, advancing understanding of its geometric structure.
Contribution
It establishes the irreducibility of the Hilbert scheme of 11 points in A^3 and introduces new techniques for constructing curves on such schemes.
Findings
Hilbert scheme of 11 points in A^3 is irreducible
Develops new methods for producing curves on Hilbert schemes
Enhances understanding of the geometry of point schemes
Abstract
We prove that the Hilbert scheme of 11 points on a smooth threefold is irreducible. In the course of the proof, we present several known and new techniques for producing curves on the Hilbert scheme.
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
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Advanced Algebra and Geometry