{"title":"The variety of flexes of plane cubics","authors":"Vladimir L. Popov","doi":"arxiv-2408.16488","DOIUrl":null,"url":null,"abstract":"Let $X$ be the variety of flexes of plane cubics. We prove that (1) $X$ is an\nirreducible rational algebraic variety endowed with an algebraic action of\n${\\rm PSL}_3$; (2) $X$ is ${\\rm PSL}_3$-equivariantly birationally isomorphic\nto a homogeneous fiber space over ${\\rm PSL}_3/K$ with fiber $\\mathbb P^1$ for\nsome subgroup $K$ isomorphic to the binary tetrahedral group ${\\rm\nSL}_2(\\mathbb F_3)$.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"170 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Algebraic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.16488","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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 ${\rm
SL}_2(\mathbb F_3)$.