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This content will become publicly available on July 3, 2025

Title: Castelnuovo-Mumford regularity of matrix Schubert varieties
Matrix Schubert varieties are affine varieties arising in the Schubert calculus of the complete flag variety. We give a formula for the Castelnuovo–Mumford regularity of matrix Schubert varieties, answering a question of Jenna Rajchgot. We follow her proposed strategy of studying the highest-degree homogeneous parts of Grothendieck polynomials, which we call Castelnuovo–Mumford polynomials. In addition to the regularity formula, we obtain formulas for the degrees of all Castelnuovo–Mumford polynomials and for their leading terms, as well as a complete description of when two Castelnuovo–Mumford polynomials agree up to scalar multiple. The degree of the Grothendieck polynomial is a new permutation statistic which we call the Rajchgot index; we develop the properties of Rajchgot index and relate it to major index and to weak order.  more » « less
Award ID(s):
2344764 1855135 1854225
NSF-PAR ID:
10521261
Author(s) / Creator(s):
; ;
Publisher / Repository:
Springer Nature
Date Published:
Journal Name:
Selecta Mathematica
Volume:
30
ISSN:
1022-1824
Page Range / eLocation ID:
66
Subject(s) / Keyword(s):
Castelnuovo–Mumford regularity Matrix Schubert variety Grothendieck polynomial Major index Weak Bruhat order Rajchgot index
Format(s):
Medium: X Other: pdf
Sponsoring Org:
National Science Foundation
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