Work

Fine multidegrees, universal Gröbner bases, and matrix Schubert varieties

Year: 2026

Type: article

Abstract: We give a criterion for a collection of polynomials to be a universal Gröbner basis for an ideal in terms of the multidegree of the closure of the corresponding affine variety in . This criterion can be used to give simple proofs of several existing results on universal Gröbner bases. We introduce fine Schubert polynomials, which record the multidegrees of the closures of matrix Schubert varieties in . We compute the fine Schubert polynomials of permutations where the coefficients of the Schubert polynomials of and are all either 0 or 1, and we use this to give a universal Gröbner basis for the ideal of the matrix Schubert variety of such a permutation.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70647

Authors: Daoji Huang, Matt Larson

Institutions: University of Massachusetts Amherst, Princeton University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funder: National Science Foundation