{"title":"反霍奇八面体","authors":"Mirko Mauri","doi":"arxiv-2409.01800","DOIUrl":null,"url":null,"abstract":"The perverse-Hodge octahedron is a 3D enhancement of the Hodge diamond of a\ncompact hyperk\\\"{a}hler manifold. Its existence is equivalent to Nagai's\nconjecture, which holds for all known deformation types. The octahedron appears\nimplicitly in Huybrechts-Mauri and Shen-Yin.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"29 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Perverse-Hodge octahedron\",\"authors\":\"Mirko Mauri\",\"doi\":\"arxiv-2409.01800\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The perverse-Hodge octahedron is a 3D enhancement of the Hodge diamond of a\\ncompact hyperk\\\\\\\"{a}hler manifold. Its existence is equivalent to Nagai's\\nconjecture, which holds for all known deformation types. The octahedron appears\\nimplicitly in Huybrechts-Mauri and Shen-Yin.\",\"PeriodicalId\":501063,\"journal\":{\"name\":\"arXiv - MATH - Algebraic Geometry\",\"volume\":\"29 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-03\",\"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-2409.01800\",\"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-2409.01800","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The perverse-Hodge octahedron is a 3D enhancement of the Hodge diamond of a
compact hyperk\"{a}hler manifold. Its existence is equivalent to Nagai's
conjecture, which holds for all known deformation types. The octahedron appears
implicitly in Huybrechts-Mauri and Shen-Yin.
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