Dimension of the singularity category of a variety with rational singularities

TL;DR

This paper investigates the Rouquier dimension of the singularity category for varieties with rational singularities, providing an upper bound when the singular locus has dimension at most one.

Contribution

It establishes an upper bound for the Rouquier dimension of the singularity category of varieties with rational singularities and low-dimensional singular locus.

Findings

Derived an explicit upper bound for the Rouquier dimension

Focused on varieties with rational singularities and singular locus dimension ≤ 1

Contributed to understanding the complexity of singularity categories

Abstract

In this paper, we study the Rouquier dimension of the singularity category of a variety with rational singularity. We construct an upper bound for the dimension of $\mathrm{D}_{\mathrm{sg}}(X)$ if $X$ has at worst rational singularities and $\dim X_{\mathrm{sing}} \leq 1$.