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Regular version of the site

Article

Singular Curves and Quasi-hereditary Algebras

International Mathematics Research Notices. 2017. No. 3. P. 895-920.
Burban I., Drozd Y., Gavran V.

In this article we construct a categorical resolution of singularities of an excellent reduced curve $X$, introducing a certain sheaf of orders on $X$. This categorical resolution is shown to be a recollement of the derived category of coherent sheaves on the normalization of $X$ and the derived category of finite length modules over a certain artinian quasi-hereditary ring $Q$ depending purely on the local singularity types of $X$. 
Using this technique, we prove several statements on the Rouquier dimension of the derived category of coherent sheaves on $X$. Moreover, in the case $X$ is rational and projective we construct a finite dimensional quasi-hereditary algebra $\Lambda$ such that the triangulated category of perfect complexes on $X$ embeds into $D^b(\Lambda−mod)$ as a full subcategory.