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arXiv · 2506.21939

Polynomial Bridgeland Stability Conditions on the Category of Coherent Sheaves

Rémi Delloque
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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.

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Rémi Delloque. 2025-06-27. Polynomial Bridgeland Stability Conditions on the Category of Coherent Sheaves. https://arxiv.org/abs/2506.21939

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