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# schubertRegularity -- compute the Castelnuovo-Mumford regularity of the quotient by a Schubert determinantal ideal or ASM ideal

## Synopsis

• Usage:
schubertRegularity w
schubertRegularity A
• Inputs:

## Description

Given a partial alternating sign matrix or a permutation in 1-line notation, computes the Castelnuovo-Mumford regularity of the quotient by the corresponding alternating sign matrix ideal or Schubert determinantal ideal. In the case of a permutation in 1-line notation, computes the Castelnuovo-Mumford regularity of the corresponding Schubert determinantal ideal by implementing Theorem 1.1 of

• Oliver Pechenik, David Speyer, and Anna Weigandt, Castelnuovo-Mumford regularity of matrix Schubert varieties, arXiv:2111.10681

In the case of a partial permutation, computes the regularity using the antidiagonal initial ideal, a valid strategy in light of

• Aldo Conca and Matteo Varbaro, Square-free Gröbner degenerations, arXiv:1805.11923, Invent. Math. 221 (2020), no. 3, 713–730.

 i1 : w = {2,3,5,1,4} o1 = {2, 3, 5, 1, 4} o1 : List i2 : schubertRegularity w o2 = 2 i3 : A = matrix{{0,0,1,0,0},{1,0,0,0,0},{0,1,-1,1,0},{0,0,0,0,1},{0,0,1,0,0}}; 5 5 o3 : Matrix ZZ <-- ZZ i4 : schubertRegularity A o4 = 2

## Ways to use schubertRegularity :

• schubertRegularity(List)
• schubertRegularity(Matrix)

## For the programmer

The object schubertRegularity is .