Triangulated characterizations of singularities

Fuente: arXiv
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Main Authors: Lank, Pat, Venkatesh, Sridhar
Format: Preprint
Published: 2024
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author Lank, Pat
Venkatesh, Sridhar
author_facet Lank, Pat
Venkatesh, Sridhar
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2405_04389
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Triangulated characterizations of singularities
Lank, Pat
Venkatesh, Sridhar
Algebraic Geometry
Commutative Algebra
14F08 (primary), 14B05 (secondary), 14F17, 14A30, 14E15, 18G80
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.
title Triangulated characterizations of singularities
topic Algebraic Geometry
Commutative Algebra
14F08 (primary), 14B05 (secondary), 14F17, 14A30, 14E15, 18G80
url https://arxiv.org/abs/2405.04389