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The Escobar-Klein-Weigandt Conjecture on Cohen-Macaulay ASM Varieties

Escobar, Klein and Weigandt proved that gradedness of an ASM weak order interval, constancy of Coxeter length across its fibres, and equidimensionality of the associated ASM varieties are mutually equivalent, and conjectured (Conjecture 3.21) that Cohen-Macaulayness of those varieties belongs on the same list. Proved, via a $0$-Hecke monoid action on the MacNeille completion of Bruhat order and vertex-decomposability of certain unions of Knutson-Miller subword complexes.

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combinatoricsMay 8, 2026Significance 15/100Registry: unreviewed

The Escobar-Klein-Weigandt Conjecture on Cohen-Macaulay ASM Varieties

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Escobar, Klein and Weigandt proved that gradedness of an ASM weak order interval, constancy of Coxeter length across its fibres, and equidimensionality of the associated ASM varieties are mutually equivalent, and conjectured (Conjecture 3.21) that Cohen-Macaulayness of those varieties belongs on the same list. Proved, via a $0$-Hecke monoid action on the MacNeille completion of Bruhat order and vertex-decomposabil…

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Escobar, Klein and Weigandt proved that gradedness of an ASM weak order interval, constancy of Coxeter length across its fibres, and equidimensionality of the associated ASM varieties are mutually equivalent, and conjectured (Conjecture 3.21) that Cohen-Macaulayness of those varieties belongs on the same list. Proved, via a $0$-Hecke monoid action on the MacNeille completion of Bruhat order and vertex-decomposability of certain unions of Knutson-Miller subword complexes.

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