Universität zu Köln

Burban, Igor, Drozd, Yuriy ORCID: 0000-0002-4766-8791 and Gavran, Volodymyr (2017). Singular Curves and Quasi-hereditary Algebras. Int. Math. Res. Notices, 2017 (3). S. 895 - 921. OXFORD: OXFORD UNIV PRESS. ISSN 1687-0247

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Abstract

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 Perf(X) embeds into D-b(Lambda - mod) as a full subcategory.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Burban, Igor UNSPECIFIED UNSPECIFIED UNSPECIFIED Drozd, Yuriy UNSPECIFIED orcid.org/0000-0002-4766-8791 UNSPECIFIED Gavran, Volodymyr UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-241701
DOI:	10.1093/imrn/rnw045
Journal or Publication Title:	Int. Math. Res. Notices
Volume:	2017
Number:	3
Page Range:	S. 895 - 921
Date:	2017
Publisher:	OXFORD UNIV PRESS
Place of Publication:	OXFORD
ISSN:	1687-0247
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language CATEGORICAL RESOLUTIONS; DIMENSIONS Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/24170