Work

Schubert determinantal ideals are Hilbertian

Year: 2025

Type: article

Abstract: Abhyankar defined an ideal to be Hilbertian if its Hilbert polynomial coincides with its Hilbert function for all nonnegative integers. In 1984, he proved that the ideal of ( r + 1 ) -order minors of a generic p × q matrix is Hilbertian. We give a different proof and a generalization to the Schubert determinantal ideals introduced by Fulton in 1992. Our proof reduces to a simple upper bound for the Castelnuovo–Mumford regularity of these ideals. We further indicate the pervasiveness of the Hilbertian property in Schubert geometry.

Source: Journal of Algebra

DOI: 10.1016/j.jalgebra.2025.04.005

Authors: Ada Stelzer, Alexander Yong

Institution: University of Illinois Urbana-Champaign

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,310

Funders: National Science Foundation, Simons Foundation