Interpolation, Bridgeland stability and monomial schemes in the plane
Interpolation, Bridgeland stability and monomial schemes in the plane
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DOI：
10.1016/j.matpur.2014.02.010
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发表时间：
2013-05
期刊：
影响因子：
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通讯作者：
Izzet Coskun;J. Huizenga
中科院分区：
文献类型：
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作者：
Izzet Coskun;J. Huizenga
给定零维格式Z，高阶插值问题要求对斜率μ进行分类，使得对所有i都存在一个斜率μ向量丛E满足HI(E⊗IZ)=0.本文解决了P2中所有零维单项格式的这个问题.作为推论，我们得到了P2上点的Hilbert格式上Brill-Noether因子的稳定基轨迹的详细信息.我们证明了单项格式的Bridgland稳定流形上的壁与[2]中有效锥猜想的Mori室分解中的壁之间的对应关系.在适当的Bridgeland稳定性条件下，我们确定了单项格式理想层的Harder-Narasimhan滤波，从而得到了比最小自由分辨等其他标准分辨更适合于上同调计算的新分辨.
Given a zero-dimensional scheme Z, the higher-rank interpolation problem asks for the classification of slopes μ such that there exists a vector bundle E of slope μ satisfying H i (E⊗ I Z)= 0 for all i. In this paper, we solve this problem for all zero-dimensional monomial schemes in P 2. As a corollary, we obtain detailed information on the stable base loci of Brill–Noether divisors on the Hilbert scheme of points on P 2. We prove the correspondence between walls in the Bridgeland stability manifold and walls in the Mori chamber decomposition of the effective cone conjectured in [2] for monomial schemes. We determine the Harder–Narasimhan filtration of ideal sheaves of monomial schemes for suitable Bridgeland stability conditions and, as a consequence, obtain a new resolution better suited for cohomology computations than other standard resolutions such as the minimal free resolution.