Walls and Asymptotics for Bridgeland Stability Conditions on Threefolds

M Jardim, Antony Maciocia*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider Bridgeland stability conditions for three-folds conjectured by Bayer-Macri-Toda in the case of Picard rank one. We study the differential geometry of numerical walls, characterizing when they are bounded, discussing possible intersections, and showing that they are essentially regular.
Next, we prove that walls within a certain region of the upper half plane that parameterized geometric stability conditions must always intersect the curve given by the vanishing of the slope function and, for a fixed value of s, have a maximum turning point there. We then use these facts to prove that Gieseker
semistability is equivalent to a strong form of asymptotic semistability along a class of paths in the upper half plane, and show how to find large families of walls. We illustrate how to compute all of the walls and describe the Bridgeland
moduli spaces for the Chern character (2,0,-1,0) on complex projective 3-space in a suitable region of the upper half plane.
Original languageEnglish
Number of pages69
JournalÉpijournal de Géométrie Algébrique
Publication statusAccepted/In press - 4 Aug 2022

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