English

Stability conditions on fibred threefolds

Algebraic Geometry 2022-06-22 v2

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.

Keywords

Cite

@article{arxiv.2201.13251,
  title  = {Stability conditions on fibred threefolds},
  author = {Hao Max Sun},
  journal= {arXiv preprint arXiv:2201.13251},
  year   = {2022}
}

Comments

typos corrected

R2 v1 2026-06-24T09:10:51.023Z