Stability conditions on Fano threefolds of Picard number 1
By Chunyi Li. Journal of the European Mathematical Society (Print), 2015
72 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/9e02cc68efd517dd1891371b683cc024598b92fe
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In Algebra and Number Theory
- Emanuele Macrì
- Benjamin Schmidt
- Arend Bayer
- Xiaolei Zhao
- M. Bernardara
- P. Stellari
- Mart'i Lahoz
- Michael Usher
In Applied Mathematics
- Emanuele Macrì
- Benjamin Schmidt
- P. Stellari
- M. Bernardara
- Xiaolei Zhao
- Arend Bayer
- Chunyi Li
- Mart'i Lahoz
In Geometry and Topology
- Emanuele Macrì
- Chunyi Li
- Benjamin Schmidt
- P. Stellari
- Arend Bayer
- Xiaolei Zhao
- M. Bernardara
- Mart'i Lahoz
Citations in the corpus
- Lectures on Bridgeland Stability (2016, methodology): “ts of abelian threefolds (this includes examples of Calabi-Yau threefolds which are simply-connected). The latest progress is the proof of the conjecture for all Fano threefolds of Picard rank one in [Li19] and a proofof a modified version for all Fano threefolds independently in [BMSZ17] and [Piy17]”
- Bridgeland Stability Conditions on Fano Threefolds (2016, methodology): “The idea of the proof of Theorem 1.1 follows along the same lines as in [Li15], by using an Euler characteristic estimate.”
- Stability conditions on Kuznetsov components (2017, background): “In [Li19], stability conditions have been constructed on the whole category Db(X), when X is a Fano threefold of Picard rank one (and in general in [Piy17, BMSZ17]).”
- On stability conditions for the quintic threefold (2018, methodology): “Stability conditions are only known to exist on few families of smooth projective threefolds: Fano threefolds [Mac14,Sch13,Li15,Piy16,BMSZ17], Abelian threefolds [MP13a,MP13b,BMS16] and Kummer type threefolds [BMS16].”