Serre dimension and stability conditions
arXiv:1907.10981 · doi:10.1007/s00209-021-02718-6
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.
22 pages. final version to appear in Mathematische Zeitschrift