立方曲面的八叉法线形式及其在自动形态中的应用

IF 0.5 4区数学 Q3 MATHEMATICS

Geometriae Dedicata Pub Date : 2024-07-20 DOI:10.1007/s10711-024-00931-1

China Kaneko

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引用次数: 0

摘要

我们将证明，在任何特征中，每一个非星形立方曲面都与八叉法式给出的曲面投影同构。在 Panizzut 等人的著作（LeMatematiche 75(2), 2020）中，只有在特征为 0 的情况下，通过穷举式计算机搜索，才发现了这种正则表达式。我们提供了一个概念性的解释，它的额外好处是不含特征。作为应用，我们给出了 Dolgachev 和 Duncan (Compos Math 25(1):1-59, 1972) 中定义的立方曲面粗模态空间的八叉法线形式，它保留了关于自动形的大部分特化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

The octanomial normal forms of cubic surfaces with applications to automorphisms

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The octanomial normal forms of cubic surfaces with applications to automorphisms

We will show that in any characteristic every nonsingular cubic surface is projectively isomorphic to the surface given by the octanomial normal form. This normal form is discovered in Panizzut et al. (LeMatematiche 75(2), 2020) only in characteristic 0 by exhaustive computer search. We offer a conceptual explanation that has the added benefit of being characteristic free. As an application, we give octanomial normal forms of the strata of the coarse moduli space of cubic surfaces defined in Dolgachev and Duncan (Compos Math 25(1):1–59, 1972) which preserve most specialization with respect to automorphisms.

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来源期刊

Geometriae Dedicata 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Geometriae Dedicata concentrates on geometry and its relationship to topology, group theory and the theory of dynamical systems. Geometriae Dedicata aims to be a vehicle for excellent publications in geometry and related areas. Features of the journal will include: A fast turn-around time for articles. Special issues centered on specific topics. All submitted papers should include some explanation of the context of the main results. Geometriae Dedicata was founded in 1972 on the initiative of Hans Freudenthal in Utrecht, the Netherlands, who viewed geometry as a method rather than as a field. The present Board of Editors tries to continue in this spirit. The steady growth of the journal since its foundation is witness to the validity of the founder''s vision and to the success of the Editors'' mission.