Antidiagonal Initial Complexes of Infinite Matrix Schubert Varieties are Cohen-Macaulay

TL;DR

This paper proves that certain infinite matrix Schubert varieties have Cohen-Macaulay properties, expanding the class of known non-Noetherian Cohen-Macaulay rings through combinatorial and algebraic methods.

Contribution

It establishes Cohen-Macaulayness of initial complexes of infinite matrix Schubert varieties for specific permutations, introducing new non-Noetherian Cohen-Macaulay examples.

Findings

Initial complexes are Cohen-Macaulay under antidiagonal term order

Provides conditions for Stanley-Reisner rings to be Cohen-Macaulay

Expands understanding of non-Noetherian Cohen-Macaulay rings

Abstract

We show that, under certain constraints, the Stanley-Reisner ring of an infinite simplicial complex is Cohen-Macaulay in the sense of ideals and weak Bourbaki unmixed. We apply this result to prove the wanted claim -- that initial complexes of matrix Schubert varieties corresponding to infinite permutations in $S_{\infty}$ with respect to an antidiagonal term order are Cohen-Macaulay (in the same sense), giving rise to new examples of non-Noetherian Cohen-Macaulay rings.