Posets and fractional Calabi–Yau categories

Frédéric Chapoton

doi:10.5802/mrr.21

Frédéric Chapoton ¹

¹ Institut de Recherche Mathématique Avancée, UMR 7501 Université de Strasbourg et CNRS, 7 rue René-Descartes, 67000 Strasbourg, France

Mathematics Research Reports, Volume 6 (2025), pp. 1-16.

Abstract

This article deals with a relationship between derived categories of modules over some partially ordered sets and triangulated categories arising from quasi-homogeneous isolated singularities. It produces heuristics for the existence of derived equivalences between posets, using the geometric category as an auxiliary intermediate. The notion of Weight plays a central role as a simple footprint of the derived categories under consideration.

Received: 2024-09-02
Revised: 2024-11-22
Published online: 2025-02-03

DOI: 10.5802/mrr.21

Classification: 06A11, 18G80, 14B05
Mots-clés : poset, quasi-homogeneous singularity, derived category, derived equivalence, isolated singularity, fractional Calabi–Yau category

Author's affiliations:

Frédéric Chapoton ¹

¹ Institut de Recherche Mathématique Avancée, UMR 7501 Université de Strasbourg et CNRS, 7 rue René-Descartes, 67000 Strasbourg, France

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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Frédéric Chapoton. Posets and fractional Calabi–Yau categories. Mathematics Research Reports, Volume 6 (2025), pp. 1-16. doi : 10.5802/mrr.21. https://mrr.centre-mersenne.org/articles/10.5802/mrr.21/

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