{"title":"实际双延期的周期","authors":"Richard Hain","doi":"arxiv-2408.13997","DOIUrl":null,"url":null,"abstract":"A real biextension is a real mixed Hodge structure that is an extension of\nR(0) by a mixed Hodge structure with weights $-1$ and $-2$. A unipotent real\nbiextension over an algebraic manifold is a variation of mixed Hodge structure\nover it, each of whose fibers is a real biextension and whose weight graded\nquotients are do not vary. We show that if a unipotent real biextension has non\nabelian monodromy, then its ``general fiber'' does not split. This result is a\ntool for investigating the boundary behaviour of normal functions and is\napplied in arXiv:2408.07809 to study the boundary behaviour of the normal\nfunction of the Ceresa cycle.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"60 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Periods of Real Biextensions\",\"authors\":\"Richard Hain\",\"doi\":\"arxiv-2408.13997\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A real biextension is a real mixed Hodge structure that is an extension of\\nR(0) by a mixed Hodge structure with weights $-1$ and $-2$. A unipotent real\\nbiextension over an algebraic manifold is a variation of mixed Hodge structure\\nover it, each of whose fibers is a real biextension and whose weight graded\\nquotients are do not vary. We show that if a unipotent real biextension has non\\nabelian monodromy, then its ``general fiber'' does not split. This result is a\\ntool for investigating the boundary behaviour of normal functions and is\\napplied in arXiv:2408.07809 to study the boundary behaviour of the normal\\nfunction of the Ceresa cycle.\",\"PeriodicalId\":501063,\"journal\":{\"name\":\"arXiv - MATH - Algebraic Geometry\",\"volume\":\"60 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-26\",\"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-2408.13997\",\"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-2408.13997","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A real biextension is a real mixed Hodge structure that is an extension of
R(0) by a mixed Hodge structure with weights $-1$ and $-2$. A unipotent real
biextension over an algebraic manifold is a variation of mixed Hodge structure
over it, each of whose fibers is a real biextension and whose weight graded
quotients are do not vary. We show that if a unipotent real biextension has non
abelian monodromy, then its ``general fiber'' does not split. This result is a
tool for investigating the boundary behaviour of normal functions and is
applied in arXiv:2408.07809 to study the boundary behaviour of the normal
function of the Ceresa cycle.