Stability manifolds of varieties with finite Albanese morphisms

Lie Fu; Chunyi Li; Xiaolei Zhao

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arXiv · 2103.07728

Stability manifolds of varieties with finite Albanese morphisms

Lie Fu·Chunyi Li·Xiaolei Zhao

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Abstract

For a smooth projective complex variety whose Albanese morphism is finite, we show that every Bridgeland stability condition on its bounded derived category of coherent sheaves is geometric, in the sense that all skyscraper sheaves are stable with the same phase. Furthermore, we describe the stability manifolds of irregular surfaces and abelian threefolds with Picard rank one, and show that they are connected and contractible.

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Lie Fu, Chunyi Li, Xiaolei Zhao. 2021-03-13. Stability manifolds of varieties with finite Albanese morphisms. https://arxiv.org/abs/2103.07728

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