Stability conditions on Fano threefolds of Picard number one

Chunyi Li

Stability conditions on Fano threefolds of Picard number one

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arxiv 1510.04089 v2 pith:6DNXEJAA submitted 2015-10-14 math.AG

Chunyi Li This is my paper · ORCID

classification math.AG

keywords conditionsstabilityfanonumberpicardslopebogomolov-giesekerbound

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We prove the conjectural Bogomolov-Gieseker type inequality for tilt slope stable objects on each Fano threefold X of Picard number one. Based on the previous works on Bridgeland stability conditions, this induces an open subset of geometric stability conditions on D^b(X). We also get a new stronger bound for the Chern characters of slope semistable sheaves on X.

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Moduli spaces on the Kuznetsov component of Fano threefolds of index 2
math.AG 2019-08 conditional novelty 6.0 of 10

For general quartic double solids, two varieties are isomorphic if and only if their Kuznetsov components are equivalent, without assuming the equivalence has Fourier-Mumford type.

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