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

Coskun, Izzet; Hyeon, Donghoon; Park, Junyoung

doi:10.1090/proc/13470

Castelnuovo-Mumford regularity and Bridgeland stability of points in the projective plane
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by Izzet Coskun, Donghoon Hyeon and Junyoung Park

Proc. Amer. Math. Soc. 145 (2017), 4573-4583

DOI: https://doi.org/10.1090/proc/13470

Published electronically: July 27, 2017

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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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