TY - JOUR

T1 - Vertical Asymptotics for Bridgeland Stability Conditions on 3-Folds

AU - Jardim, Marcos

AU - Maciocia, Antony

AU - Martinez, Cristian

N1 - Funding Information:
M.J. is supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) grant number 302889/2018-3 and the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Thematic Project 2018/21391-1. C.M. is supported by the FAPESP grant number 2020/06938-4, which is part of the FAPESP Thematic Project 2018/21391-1.
Publisher Copyright:
© 2022 The Author(s). Published by Oxford University Press. All rights reserved.

PY - 2023/8/1

Y1 - 2023/8/1

N2 - 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(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.

AB - 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(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.

UR - http://www.scopus.com/inward/record.url?scp=85172316797&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85172316797&partnerID=8YFLogxK

U2 - 10.1093/imrn/rnac236

DO - 10.1093/imrn/rnac236

M3 - Article

SN - 1073-7928

VL - 2023

SP - 14699

EP - 14751

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 17

ER -