CASTELNUOVO-MUMFORD REGULARITY AND BRIDGELAND STABILITY OF POINTS IN THE PROJECTIVE PLANE
journal contributionposted on 28.06.2018 by I Coskun, D Hyeon, J Park
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In this paper, we study the relation between Castelnuovo-Mumford regularity and Bridgeland stability for the Hilbert scheme of n points on P-2. For the largest [n/2] 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.