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Vertical Asymptotics for Bridgeland Stability Conditions on 3-Folds
- Source :
- International Mathematics Research Notices.
- Publication Year :
- 2022
- Publisher :
- Oxford University Press (OUP), 2022.
-
Abstract
- Let $X$ be a smooth projective threefold of Picard number one for which the generalized Bogomlov-Gieseker inequality holds. We characterize the limit Bridgeland semistable objects at large volume in the vertical region of the geometric stability conditions associated to $X$ in complete generality and provide examples of asymptotically semistable objects. In the case of the projective space and $ch^\beta(E)=(-R,0,D,0)$, we prove that there are only a finite number of nested walls in the $(\alpha,s)$-plane. Moreover, when $R=0$ the only semistable objects in the outermost chamber are the 1-dimensional Gieseker semistable sheaves, and when $\beta=0$ there are no semistable objects in the innermost chamber. In both cases, the only limit semistable objects of the form $E$ or $E[1]$ (where $E$ is a sheaf) that do not get destabilized until the innermost wall are precisely the (shifts of) instanton sheaves.<br />Comment: 44 pages, comments welcome!
Details
- ISSN :
- 16870247 and 10737928
- Database :
- OpenAIRE
- Journal :
- International Mathematics Research Notices
- Accession number :
- edsair.doi.dedup.....11f8d63b3aeeeb5445ed15d4a9b89086