具有正特征的有限自同构群的Enriques曲面

IF 1.2 1区数学 Q1 MATHEMATICS

Algebraic Geometry Pub Date : 2017-03-24 DOI:10.14231/ag-2019-027

G. Martin

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引用次数: 24

摘要

我们对具有光滑K3覆盖和有限自同构群的任意正特征的Enriques曲面进行了分类。除了一些类型在小特征上缺失外，分类与在复数上相同。此外，我们给出了这些曲面的模的完整描述。最后，我们在素域$\mathbb{F}_p$和$\mathbb{Q}$上实现了所有类型的具有有限自同构群的Enriques曲面，只要它们存在。

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Enriques surfaces with finite automorphism group in positive characteristic

We classify Enriques surfaces with smooth K3 cover and finite automorphism group in arbitrary positive characteristic. The classification is the same as over the complex numbers except that some types are missing in small characteristics. Moreover, we give a complete description of the moduli of these surfaces. Finally, we realize all types of Enriques surfaces with finite automorphism group over the prime fields $\mathbb{F}_p$ and $\mathbb{Q}$ whenever they exist.

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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.