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arXiv · 2601.02612

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

Anna Natalie Chlopecki·Nathaniel Gallup·Jason Meintjes
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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.

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Anna Natalie Chlopecki, Nathaniel Gallup, Jason Meintjes. 2026-01-06. Antidiagonal Initial Complexes of Infinite Matrix Schubert Varieties are Cohen-Macaulay. https://arxiv.org/abs/2601.02612

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