Serre dimension and stability conditions

We study relations between the Serre dimension defined as the growth of the 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 Serre dimension lower than one with a Gepner type stability condition.

Automated summary

This study explores the relationship between the growth of the entropy of the Serre functor and the global dimension of Bridgeland stability conditions, as well as proving a fundamental inequality between the Serre dimension and the infimum of the global dimensions. Furthermore, Gepner type stability conditions on fractional Calabi-Yau categories are characterized via the Serre dimension, and triangulated categories with a Serre dimension lower than one and a Gepner type stability condition are classified.