Dimension of the singularity category of a variety with rational   singularities
  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 $\dim X_{\mathrm{sing}} \leq 1$. 
Wahei Hara
math.AG math.AC