Hilbert Schemes with Two Borel-fixed Points in Arbitrary Characteristic

2021/07/05 by Andrew P. Staal, Staal, Andrew P.
Mathematics · #13C05 #13C70 #14D22 #14J10 #14Q15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2107.02204

openalex publication_date 2021/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the recent classification of Hilbert schemes with two Borel-fixed points to arbitrary characteristic. We accomplish this by synthesizing Reeves' algorithm for generating strongly stable ideals with the basic properties of Borel-fixed ideals and our previous work classifying Hilbert schemes with unique Borel-fixed points.

Related

• Hilbert schemes with two Borel-fixed points
• An efficient implementation of the algorithm computing the Borel-fixed\n points of a Hilbert scheme
• Quasi-Stable ideals and Borel-fixed ideals with a given Hilbert\n Polynomial
• Weighted Borel Generators
• New components of Hilbert schemes of points and 2-step ideals