| Full text | |
| Author(s): |
Jardim, Marcos
;
Maciocia, Antony
;
Martinez, Cristian
Total Authors: 3
|
| Document type: | Journal article |
| Source: | INTERNATIONAL MATHEMATICS RESEARCH NOTICES; v. N/A, p. 53-pg., 2022-08-31. |
| Abstract | |
Let X be a smooth projective threefold of Picard number one for which the generalized Bogomolov-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. (AU) | |
| FAPESP's process: | 18/21391-1 - Gauge theory and algebraic geometry |
| Grantee: | Marcos Benevenuto Jardim |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 20/06938-4 - Geometry of moduli spaces of sheaves via wall-crossing |
| Grantee: | Cristian Mauricio Martinez Esparza |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |