Hilbert曲面方案上的重言丛的Segre类

IF 1.2 1区数学 Q1 MATHEMATICS

Algebraic Geometry Pub Date : 2017-08-21 DOI:10.14231/AG-2019-010

C. Voisin

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引用次数: 26

摘要

我们首先基于一个简单的几何论证，给出了Marian、Oprea和Pandharipande在配备有线丛的$K3$曲面的Hilbert方案上的重言丛的顶Segre类上的结果的另一个证明。然后，我们转向$K3$曲面在某一点上的爆破，并在一定范围内建立相应的顶级Segre类的消失结果。这至少在理论上确定了｛\rm-Pic｝\，\ Sigma$中的任何对$（\ Sigma，H），\，H\的重言丛的所有顶级Segre类。

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Segre classes of tautological bundles on Hilbert schemes of surfaces

We first give an alternative proof, based on a simple geometric argument, of a result of Marian, Oprea and Pandharipande on top Segre classes of the tautological bundles on Hilbert schemes of $K3$ surfaces equipped with a line bundle. We then turn to the blow-up of $K3$ surface at one point and establish vanishing results for the corresponding top Segre classes in a certain range. This determines, at least theoretically, all top Segre classes of tautological bundles for any pair $(\Sigma,H),\,H\in {\rm Pic}\,\Sigma$.

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来源期刊

Algebraic Geometry Mathematics-Geometry and Topology

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

52 weeks

期刊介绍： This journal is an open access journal owned by the Foundation Compositio Mathematica. The purpose of the journal is to publish first-class research papers in algebraic geometry and related fields. All contributions are required to meet high standards of quality and originality and are carefully screened by experts in the field.