论文标题
在希尔伯特的点方案上，大型和NEF重言式矢量束
Big and Nef Tautological Vector Bundles over the Hilbert Scheme of Points
论文作者
论文摘要
我们研究了在表面上的Hilbert方案上的重言式矢量束。对于每个k琐碎的表面，我们写下一个简单的标准，以确保重言式捆绑包大且NEF，并通过示例进行说明。在K3案例中，我们将Bini，Boissière和Flamini的最新结构和结果从2和3分的希尔伯特方案扩展到了任意数量。在K-繁琐的表面中，最多的含量表面的情况是最涉及的。我们的技术适用于其他光滑的投射表面，包括K3的爆炸和一般类型的最小表面，以及曲线的准时引用方案。
We study tautological vector bundles over the Hilbert scheme of points on surfaces. For each K-trivial surface, we write down a simple criterion ensuring that the tautological bundles are big and nef, and illustrate it by examples. In the K3 case, we extend recent constructions and results of Bini, Boissière and Flamini from the Hilbert scheme of 2 and 3 points to an arbitrary number of points. Among the K-trivial surfaces, the case of Enriques surfaces is the most involved. Our techniques apply to other smooth projective surfaces, including blowups of K3s and minimal surfaces of general type, as well as to the punctual Quot schemes of curves.
