Serre dimension and stability conditions
Algebraic Geometry
2021-03-09 v3 Category Theory
Abstract
We study relations between the Serre dimension defined as the growth of entropy of the Serre functor and the global dimension of Bridgeland stability conditions due to Ikeda-Qiu. A fundamental inequality between the Serre dimension and the infimum of the global dimensions is proved. Moreover, we characterize Gepner type stability conditions on fractional Calabi-Yau categories via the Serre dimension, and classify triangulated categories of the Serre dimension lower than one with a Gepner type stability condition.
Cite
@article{arxiv.1907.10981,
title = {Serre dimension and stability conditions},
author = {Kohei Kikuta and Genki Ouchi and Atsushi Takahashi},
journal= {arXiv preprint arXiv:1907.10981},
year = {2021}
}
Comments
22 pages. final version to appear in Mathematische Zeitschrift