Polynomial Bridgeland Stability Conditions on the Category of Coherent Sheaves

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–Hölder 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.