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arXiv · 2201.13251

Stability conditions on fibred threefolds

Hao Max Sun
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Abstract

We give a conjectural construction of Bridgeland stability conditions on the derived category of fibred threefolds. The construction depends on a conjectural Bogomolov-Gieseker type inequality for certain stable complexes. It can be considered as a relative version of the construction of Bayer, Macr\`i and Toda. We prove the conjectural Bogomolov-Gieseker type inequality in the case of relative projective planes over curves. This gives the the existence of Bridgeland stability conditions on such threefolds.

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Hao Max Sun. 2022-01-31. Stability conditions on fibred threefolds. https://arxiv.org/abs/2201.13251

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