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arXiv · 1907.10981

Serre dimension and stability conditions

Kohei Kikuta·Genki Ouchi·Atsushi Takahashi
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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.

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Kohei Kikuta, Genki Ouchi, Atsushi Takahashi. 2021-03-06. Serre dimension and stability conditions. https://doi.org/10.1007/s00209-021-02718-6

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