Posets and Fractional Calabi-Yau Categories

TL;DR

This paper explores the connection between derived categories of modules over posets and triangulated categories from singularities, proposing heuristics for derived equivalences using geometric categories and the concept of Weight.

Contribution

It introduces a novel approach to determine derived equivalences between posets by leveraging geometric categories and the notion of Weight as a key invariant.

Findings

Heuristics for derived equivalences between posets

Use of geometric categories as intermediates

Weight as an invariant for derived categories

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.