Triangulated characterizations of singularities
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.
Cite
@article{arxiv.2405.04389,
title = {Triangulated characterizations of singularities},
author = {Pat Lank and Sridhar Venkatesh},
journal= {arXiv preprint arXiv:2405.04389},
year = {2025}
}
Comments
Current: Final version, to appear in Nagoya Math. J., Previous: Removed properness assumptions, removed Section 4, improved exposition