{"title":"具有交映自动形态的立方四面体","authors":"Kenji Koike","doi":"arxiv-2409.08448","DOIUrl":null,"url":null,"abstract":"We determine projective equations of smooth complex cubic fourfolds with\nsymplectic automorphisms by classifying 6-dimensional projective\nrepresentations of Laza and Zheng's 34 groups. In particular, we determine the\nnumber of irreducible components for moduli spaces of cubic fourfolds with\nsymplectic actions by these groups. We also discuss the fields of definition of\ncubic fourfolds in six maximal cases.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"211 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Cubic fourfolds with symplectic automorphisms\",\"authors\":\"Kenji Koike\",\"doi\":\"arxiv-2409.08448\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We determine projective equations of smooth complex cubic fourfolds with\\nsymplectic automorphisms by classifying 6-dimensional projective\\nrepresentations of Laza and Zheng's 34 groups. In particular, we determine the\\nnumber of irreducible components for moduli spaces of cubic fourfolds with\\nsymplectic actions by these groups. We also discuss the fields of definition of\\ncubic fourfolds in six maximal cases.\",\"PeriodicalId\":501063,\"journal\":{\"name\":\"arXiv - MATH - Algebraic Geometry\",\"volume\":\"211 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-13\",\"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-2409.08448\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Algebraic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.08448","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We determine projective equations of smooth complex cubic fourfolds with
symplectic automorphisms by classifying 6-dimensional projective
representations of Laza and Zheng's 34 groups. In particular, we determine the
number of irreducible components for moduli spaces of cubic fourfolds with
symplectic actions by these groups. We also discuss the fields of definition of
cubic fourfolds in six maximal cases.
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