型超卡勒变体上的刚性稳定向量束

IF 1.1 2区数学 Q1 MATHEMATICS Journal of the Institute of Mathematics of Jussieu Pub Date : 2023-12-22 DOI:10.1017/s1474748023000452

Kieran G. O’Grady

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引用次数: 0

摘要

我们证明了具有某些离散不变式的 $K3^{[n]}$ 型一般极化超凯勒（HK）变上斜坡稳定向量束的存在性和单一性，条件是向量束的秩和前两个车恩类满足某些相等性。后一种假设乍一看似乎限制性很大，但事实上，我们可能已经列出了几乎所有斜率稳定的刚性投影超同构向量束，它们都在模量为 20 美元的 $K3^{[n]}$ 型极化 HK varieties 上。

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RIGID STABLE VECTOR BUNDLES ON HYPERKÄHLER VARIETIES OF TYPE

We prove existence and unicity of slope-stable vector bundles on a general polarized hyperkähler (HK) variety of type

$K3^{[n]}$

with certain discrete invariants, provided the rank and the first two Chern classes of the vector bundle satisfy certain equalities. The latter hypotheses at first glance appear to be quite restrictive, but, in fact, we might have listed almost all slope-stable rigid projectively hyperholomorphic vector bundles on polarized HK varieties of type

$K3^{[n]}$

with

$20$

moduli.

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来源期刊

Journal of the Institute of Mathematics of Jussieu 数学-数学

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of the Institute of Mathematics of Jussieu publishes original research papers in any branch of pure mathematics; papers in logic and applied mathematics will also be considered, particularly when they have direct connections with pure mathematics. Its policy is to feature a wide variety of research areas and it welcomes the submission of papers from all parts of the world. Selection for publication is on the basis of reports from specialist referees commissioned by the Editors.

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