Affine homogeneous varieties and suspensions

IF 1.2 3区数学 Q1 MATHEMATICS

Research in the Mathematical Sciences Pub Date : 2024-03-22 DOI:10.1007/s40687-024-00438-x

引用次数: 0

Abstract

An algebraic variety X is called a homogeneous variety if the automorphism group \({{\,\textrm{Aut}\,}}(X)\) acts on X transitively, and a homogeneous space if there exists a transitive action of an algebraic group on X. We prove a criterion of smoothness of a suspension to construct a wide class of homogeneous varieties. As an application, we give criteria for a Danielewski surface to be a homogeneous variety and a homogeneous space. Also, we construct affine suspensions of arbitrary dimension that are homogeneous varieties but not homogeneous spaces.

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仿射同质变种和悬浮物

摘要如果自变群 \({{\,\textrm{Aut}\,}}(X)\)瞬时作用于 X，则代数簇 X 称为同质簇；如果代数群的瞬时作用存在于 X，则代数簇 X 称为同质空间。作为应用，我们给出了达尼埃莱夫斯基曲面是同质变种和同质空间的标准。此外，我们还构造了任意维度的仿射悬浮，这些悬浮是同质元，但不是同质空间。

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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来源期刊

Research in the Mathematical Sciences Mathematics-Computational Mathematics

CiteScore

2.00

自引率

8.30%

发文量

期刊介绍： Research in the Mathematical Sciences is an international, peer-reviewed hybrid journal covering the full scope of Theoretical Mathematics, Applied Mathematics, and Theoretical Computer Science. The Mission of the Journal is to publish high-quality original articles that make a significant contribution to the research areas of both theoretical and applied mathematics and theoretical computer science. This journal is an efficient enterprise where the editors play a central role in soliciting the best research papers, and where editorial decisions are reached in a timely fashion. Research in the Mathematical Sciences does not have a length restriction and encourages the submission of longer articles in which more complex and detailed analysis and proofing of theorems is required. It also publishes shorter research communications (Letters) covering nascent research in some of the hottest areas of mathematical research. This journal will publish the highest quality papers in all of the traditional areas of applied and theoretical areas of mathematics and computer science, and it will actively seek to publish seminal papers in the most emerging and interdisciplinary areas in all of the mathematical sciences. Research in the Mathematical Sciences wishes to lead the way by promoting the highest quality research of this type.