一个直接证明环面秩$2$束在射影空间上是分裂的

Pub Date : 2020-09-03 DOI:10.7146/math.scand.a-121452

David Stapleton

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引用次数: 0

摘要

本文的重点是给出一个简短的，直接的证明，秩$2$环矢量束在$n$维射影空间上分裂，当$n$至少为$3$时。这个结果最初是由Bertin和Elencwajg完成的，Kaneyama、Klyachko和ilten - s也有相关的工作。这个想法是，在可能扭曲矢量束之后，有一个截面是一个完整的交叉点。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A direct proof that toric rank $2$ bundles on projective space split

The point of this paper is to give a short, direct proof that rank $2$ toric vector bundles on $n$-dimensional projective space split once $n$ is at least $3$. This result is originally due to Bertin and Elencwajg, and there is also related work by Kaneyama, Klyachko, and Ilten-Süss. The idea is that, after possibly twisting the vector bundle, there is a section which is a complete intersection.

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