Polynomial Bridgeland Stability Conditions on the Category of Coherent Sheaves

Abstract

In this short note, we provide a broad class of examples of stability conditions on the category of coherent sheaves which generalise Gieseker stability. We refer to them as "adapted to coherent sheaves" and they admit Harder--Narasimhan and Jordan--H\"older filtrations. We also study the particular case of Bayer's polynomial Bridgeland stability conditions, and their relation to the gauge theoretical counterpart introduced by Dervan--McCarthy--Sektnan.