{"title":"Albanese映射中的导出不变量","authors":"Federico Caucci, G. Pareschi","doi":"10.14231/ag-2019-031","DOIUrl":null,"url":null,"abstract":"Let $a_X:X\\rightarrow \\mathrm{Alb}\\, X$ be the Albanese map of a smooth complex projective variety. Roughly speaking in this note we prove that for all $i \\geq 0$ and $\\alpha\\in \\mathrm{Pic}^0\\, X$, the cohomology ranks $h^i(\\mathrm{Alb}\\, X, \\,{a_X}_* \\omega_X\\otimes P_\\alpha)$ are derived invariants. In the case of varieties of maximal Albanese dimension this proves conjectures of Popa and Lombardi-Popa -including the derived invariance of the Hodge numbers $h^{0,j}$ -- and a weaker version of them for arbitrary varieties. Finally we provide an application to derived invariance of certain irregular fibrations.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2018-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Derived invariants arising from the Albanese map\",\"authors\":\"Federico Caucci, G. Pareschi\",\"doi\":\"10.14231/ag-2019-031\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $a_X:X\\\\rightarrow \\\\mathrm{Alb}\\\\, X$ be the Albanese map of a smooth complex projective variety. Roughly speaking in this note we prove that for all $i \\\\geq 0$ and $\\\\alpha\\\\in \\\\mathrm{Pic}^0\\\\, X$, the cohomology ranks $h^i(\\\\mathrm{Alb}\\\\, X, \\\\,{a_X}_* \\\\omega_X\\\\otimes P_\\\\alpha)$ are derived invariants. In the case of varieties of maximal Albanese dimension this proves conjectures of Popa and Lombardi-Popa -including the derived invariance of the Hodge numbers $h^{0,j}$ -- and a weaker version of them for arbitrary varieties. Finally we provide an application to derived invariance of certain irregular fibrations.\",\"PeriodicalId\":48564,\"journal\":{\"name\":\"Algebraic Geometry\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2018-07-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebraic Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.14231/ag-2019-031\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebraic Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.14231/ag-2019-031","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Let $a_X:X\rightarrow \mathrm{Alb}\, X$ be the Albanese map of a smooth complex projective variety. Roughly speaking in this note we prove that for all $i \geq 0$ and $\alpha\in \mathrm{Pic}^0\, X$, the cohomology ranks $h^i(\mathrm{Alb}\, X, \,{a_X}_* \omega_X\otimes P_\alpha)$ are derived invariants. In the case of varieties of maximal Albanese dimension this proves conjectures of Popa and Lombardi-Popa -including the derived invariance of the Hodge numbers $h^{0,j}$ -- and a weaker version of them for arbitrary varieties. Finally we provide an application to derived invariance of certain irregular fibrations.
期刊介绍:
This journal is an open access journal owned by the Foundation Compositio Mathematica. The purpose of the journal is to publish first-class research papers in algebraic geometry and related fields. All contributions are required to meet high standards of quality and originality and are carefully screened by experts in the field.