Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Castelnuovo-Mumford regularity and Bridgeland stability of points in the projective plane


Authors: Izzet Coskun, Donghoon Hyeon and Junyoung Park
Journal: Proc. Amer. Math. Soc. 145 (2017), 4573-4583
MSC (2010): Primary 14C05, 13D02, 14D20; Secondary 13D99, 14D99, 14C99
DOI: https://doi.org/10.1090/proc/13470
Published electronically: July 27, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we study the relation between Castelnuovo-Mumford regularity and Bridgeland stability for the Hilbert scheme of $ n$ points on $ \mathbb{P}^2$. For the largest $ \lfloor \frac {n}{2} \rfloor $ Bridgeland walls, we show that the general ideal sheaf destabilized along a smaller Bridgeland wall has smaller regularity than one destabilized along a larger Bridgeland wall. We give a detailed analysis of the case of monomial schemes and obtain a precise relation between the regularity and the Bridgeland stability for the case of Borel fixed ideals.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 14C05, 13D02, 14D20, 13D99, 14D99, 14C99

Retrieve articles in all journals with MSC (2010): 14C05, 13D02, 14D20, 13D99, 14D99, 14C99


Additional Information

Izzet Coskun
Affiliation: Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, Illinois 60607
Email: coskun@math.uic.edu

Donghoon Hyeon
Affiliation: Department of Mathematical Sciences, Seoul National University, Seoul, Republic of Korea
Email: dhyeon@snu.ac.kr

Junyoung Park
Affiliation: Department of Mathematics, POSTECH, Pohang, Gyungbuk, Republic of Korea
Email: newshake@postech.ac.kr

DOI: https://doi.org/10.1090/proc/13470
Keywords: Castelnuovo-Mumford regularity, Hilbert schemes of points, Bridgeland stability, monomial schemes
Received by editor(s): February 22, 2016
Received by editor(s) in revised form: September 3, 2016
Published electronically: July 27, 2017
Additional Notes: The first author was partially supported by the NSF CAREER grant DMS-0950951535 and the NSF grant DMS-1500031
The second author was supported by the following grants funded by the government of Korea: NRF grant 2011-0030044 (SRC-GAIA) and NRF grant NRF-2013R1A1A2010649
Communicated by: Lev Borisov
Article copyright: © Copyright 2017 American Mathematical Society

American Mathematical Society