Brill-Noether Theory of Hilbert Schemes of Points on Surfaces
Brill-Noether Theory of Hilbert Schemes of Points on Surfaces
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曲面上点的希尔伯特方案的布里尔-诺特理论
DOI：
10.1093/imrn/rnad263
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发表时间：
2023
影响因子：
1
通讯作者：
Bayer A
中科院分区：
文献类型：
--
作者：
Bayer A
我们证明了光滑连通表面上点的Hilbert格式中的Brill-Noether轨迹在其期望维数为正时是非空的，并且它们是不可约的并且具有期望维数。更准确地说，我们考虑对的轨迹，其中在局部点需要给定数量的生成器是理想的。我们给出了两个证明。第一个使用Iarrobino对局部点阵Hilbert格式的Hilbert - samuel分层的描述，第二个是基于嵌套Hilbert格式给出的不同Brill-Noether位点之间的birational关系的归纳法。
We show that Brill–Noether loci in Hilbert scheme of points on a smooth connected surfaceare non-empty whenever their expected dimension is positive and that they are irreducible and have expected dimensions. More precisely, we consider the loci of pairs, whereis an ideal that locally at the pointofneeds a given number of generators. We give two proofs. The first uses Iarrobino’s description of the Hilbert–Samuel stratification of local punctual Hilbert schemes, and the second is based on induction via birational relationships between different Brill–Noether loci given by nested Hilbert schemes.