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Supersolvability of built lattices and Koszulness of generalized Chow rings

Part of: Algebraic combinatorics Designs and configurations

Published online by Cambridge University Press:  01 September 2025

Basile Coron Open the ORCID record for Basile Coron [Opens in a new window]
Basile Coron*
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115 Oppenheimer Lane, Princeton, NJ 08540, USA basile.coron.math@gmail.com
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Abstract

We give an explicit quadratic Gröbner basis for generalized Chow rings of supersolvable built lattices, with the help of the operadic structure on geometric lattices introduced in a previous article. This shows that the generalized Chow rings associated to minimal building sets of supersolvable lattices are Koszul. As another consequence, we get that the cohomology algebras of the components of the extended modular operad in genus $0$ are Koszul.

Keywords

operadic structuresChow rings of matroidsKoszulnesssupersolvability

MSC classification

Primary: 05B35: Matroids, geometric lattices 05E40: Combinatorial aspects of commutative algebra

Information

Type
Research Article
Information
Compositio Mathematica , Volume 161 , Issue 6 , June 2025 , pp. 1284 - 1312
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Copyright
© The Author(s), 2025. The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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