平面立方体的各种弯曲

arXiv - MATH - Algebraic Geometry Pub Date : 2024-08-29 DOI:arxiv-2408.16488

Vladimir L. Popov

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引用次数: 0

摘要

设 $X$ 是平面立方体的柔面种类。我们证明：(1) $X$ 是禀赋了${\rm PSL}_3$ 的代数作用的可逆有理代数纷；(2) $X$ 是 ${rm PSL}_3$ 上的同质纤维空间，其纤维 ${rm PSL}_3/K$ 与某个子群 $K$ 的二元四面体群 ${rmSL}_2(\mathbb F_3)$ 同构。

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The variety of flexes of plane cubics

Let $X$ be the variety of flexes of plane cubics. We prove that (1) $X$ is an irreducible rational algebraic variety endowed with an algebraic action of ${\rm PSL}_3$; (2) $X$ is ${\rm PSL}_3$-equivariantly birationally isomorphic to a homogeneous fiber space over ${\rm PSL}_3/K$ with fiber $\mathbb P^1$ for some subgroup $K$ isomorphic to the binary tetrahedral group ${\rm SL}_2(\mathbb F_3)$.

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arXiv - MATH - Algebraic Geometry

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