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TRIANGULATED CHARACTERIZATIONS OF SINGULARITIES

Part of: (Co)homology theory Birational geometry Local theory

Published online by Cambridge University Press:  24 February 2025

PAT LANK Open the ORCID record for PAT LANK [Opens in a new window]  and
SRIDHAR VENKATESH Open the ORCID record for SRIDHAR VENKATESH [Opens in a new window]
PAT LANK*
Affiliation:
Dipartimento di Matematica “F. Enriques” Università degli Studi di Milano Via Cesare Saldini 50, 20133 Milano, Italy
SRIDHAR VENKATESH
Affiliation:
Department of Mathematics University of Michigan Ann Arbor, MI 48109 United States [email protected]
*
[email protected]
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Abstract

This work presents a range of triangulated characterizations for important classes of singularities such as derived splinters, rational singularities, and Du Bois singularities. An invariant called “level” in a triangulated category can be used to measure the failure of a variety to have a prescribed singularity type. We provide explicit computations of this invariant for reduced Nagata schemes of Krull dimension one and for affine cones over smooth projective hypersurfaces. Furthermore, these computations are utilized to produce upper bounds for Rouquier dimension on the respective bounded derived categories.

Keywords

triangulated categoriesRouquier dimensionderived splintersrational singularitiesDu Bois singularities

MSC classification

Primary: 14B05: Singularities 14F17: Vanishing theorems 14E15: Global theory and resolution of singularities
Type
Article
Information
Nagoya Mathematical Journal , First View , pp. 1 - 15
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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