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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Castelnuovo-Mumford regularity and Bridgeland stability of points in the projective plane
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by Izzet Coskun, Donghoon Hyeon and Junyoung Park PDF
Proc. Amer. Math. Soc. 145 (2017), 4573-4583 Request permission

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.
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Additional Information
  • Izzet Coskun
  • Affiliation: Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, Illinois 60607
  • MR Author ID: 736580
  • Email: coskun@math.uic.edu
  • Donghoon Hyeon
  • Affiliation: Department of Mathematical Sciences, Seoul National University, Seoul, Republic of Korea
  • MR Author ID: 673409
  • Email: dhyeon@snu.ac.kr
  • Junyoung Park
  • Affiliation: Department of Mathematics, POSTECH, Pohang, Gyungbuk, Republic of Korea
  • Email: newshake@postech.ac.kr
  • 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
  • © Copyright 2017 American Mathematical Society
  • 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
  • MathSciNet review: 3691977