BIMSA > Commutative Algebra Seminar in Beijing Groebner bases of determinantal ideals I
Groebner bases of determinantal ideals I
Organizers
Ming Fang , Manolis Tsakiris , Bei Hui Yuan
Speaker
Chenqi Mou
Time
Saturday, March 30, 2024 9:30 AM - 11:30 AM
Venue
AMSS-N208
Abstract
In this talk I will introduce determinantal ideals, which are multivariate polynomial ideals generated by specific minors of a generic matrix, and their Gröbner bases with respect to the (anti-)diagonal term orders. The determinantal ideals this talk will cover include traditional, ladder, and Schubert determinantal ones. For traditional determinantal ideals, I will present how the Robinson-Schensted-Knuth (RSK) correspondence from combinatorics, combined with the straightening law, can be applied to study their Gröbner bases; for Schubert determinantal ideals defined for permutations, which is a fundamental algebraic concept in the study of Schubert calculus, I will show how to construct their Fulton generators from the permutations and identify them as Gröbner bases with respect to the anti-diagonal term orders. If time permits, I will also briefly present our recent works on the reduced Gröbner bases of Schubert determinantal ideals.