​ Groebner bases of determinantal ideals ll | Commutative Algebra Seminar in Beijing

Abstract

In this talk l will introduce determinantal ideals, which are multivariate polynomial idealsgenerated by specific minors of a generic matrix, and their Grbner 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, l will present how theRobinson-Schensted-Knuth (RSK) correspondence from combinatorics, combined with thestraightening law, can be applied to study their Grbner bases; for Schubert determinantal idealsdefined for permutations, which is a fundamental algebraic concept in the study of Schubertcalculus, l will show how to construct their Fulton generators from the permutations and identifythem as Grbner bases with respect to the anti-diagonal term orders. lf time permits, l will alsobriefly present our recent works on the reduced Grbner bases of Schubert determinantal ideals.