Bridgeland Stability Conditions on Fano Threefolds
Marcello Bernardara, Emanuele Macr\`i, Benjamin Schmidt, Xiaolei Zhao
TL;DR
This paper establishes the existence of Bridgeland stability conditions on all Fano threefolds, utilizing a strong Bogomolov inequality and extending results to some toric threefolds.
Contribution
It proves the existence of Bridgeland stability conditions on all Fano threefolds and verifies the original conjecture for certain toric threefolds.
Findings
Existence of Bridgeland stability conditions on all Fano threefolds.
Verification of the original conjecture for some toric threefolds.
Application of a strong Bogomolov inequality in the proof.
Abstract
We show the existence of Bridgeland stability conditions on all Fano threefolds, by proving a modified version of a conjecture by Bayer, Toda, and the second author. The key technical ingredient is a strong Bogomolov inequality, proved recently by Chunyi Li. Additionally, we prove the original conjecture for some toric threefolds by using the toric Frobenius morphism.
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