广义的 3 阶汐达-伊诺斯结构

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2024-08-13 DOI:10.1515/advgeom-2024-0005

Alice Garbagnati, Yulieth Prieto-Montañez

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引用次数: 0

摘要

Shioda-Inose 结构是一种几何构造，它将投影 K3 曲面与阿贝尔曲面关联起来，使它们的超越网格等距。莫里森通过考虑 K3 曲面上的特殊交映渐开线描述了这种几何构造。在莫里森之后，又有几位学者提供了明确的例子。本文的目的是将莫里森的结果和一些已知的例子推广到一个类似的几何构造中，其中涉及的不是渐开线，而是阶 3 自变量。因此，我们定义了广义的 3 阶汐达-伊诺斯结构，确定了出现在这些结构中的 K3 曲面和阿贝尔曲面，并提供了明确的例子。

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Generalized Shioda–Inose structures of order 3

A Shioda–Inose structure is a geometric construction which associates to an Abelian surface a projective K3 surface in such a way that their transcendental lattices are isometric. This geometric construction was described by Morrison by considering special symplectic involutions on the K3 surfaces. After Morrison several authors provided explicit examples. The aim of this paper is to generalize Morrison’s results and some of the known examples to an analogous geometric construction involving not involutions, but order 3 automorphisms. Therefore, we define generalized Shioda–Inose structures of order 3, we identify the K3 surfaces and the Abelian surfaces which appear in these structures and we provide explicit examples.

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.