Effective divisors on the Hilbert scheme of points in the plane and interpolation for stable bundles
Effective divisors on the Hilbert scheme of points in the plane and interpolation for stable bundles
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平面上点的希尔伯特格式的有效除数和稳定丛的插值
DOI：
10.1090/jag/652
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
J. Huizenga
中科院分区：
文献类型：
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作者：
J. Huizenga
我们计算锥的有效因子的希尔伯特计划的点在投影平面上。我们证明了许多稳定的向量丛的截面满足一个自然的插值条件，并且这些向量丛总是产生Hilbert格式的有效锥的边缘。为了做到这一点，我们给出了一个推广的盖塔定理的决议的理想层的一般收集的点在平面上。这个决议有一个自然的解释Bridgeland稳定性，我们观察到，理想层的集合点是不稳定的特殊束。通过研究特殊丛的Bridgeland稳定性，我们还表明，我们的计算的有效锥的希尔伯特计划是一致的一个猜想，预测森和Bridgeland墙之间的对应关系的希尔伯特计划。
We compute the cone of effective divisors on the Hilbert scheme of points in the projective plane. We show the sections of many stable vector bundles satisfy a natural interpolation condition, and that these bundles always give rise to the edge of the effective cone of the Hilbert scheme. To do this, we give a generalization of Gaeta's theorem on the resolution of the ideal sheaf of a general collection of points in the plane. This resolution has a natural interpretation in terms of Bridgeland stability, and we observe that ideal sheaves of collections of points are destabilized by exceptional bundles. By studying the Bridgeland stability of exceptional bundles, we also show that our computation of the effective cone of the Hilbert scheme is consistent with a conjecture which predicts a correspondence between Mori and Bridgeland walls for the Hilbert scheme.