超Kähler流形中的复Lagrangians与相对Albanese

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2020-01-01 DOI:10.1515/coma-2020-0106

I. Biswas, T. G'omez, André G. Oliveira

{"title":"超Kähler流形中的复Lagrangians与相对Albanese","authors":"I. Biswas, T. G'omez, André G. Oliveira","doi":"10.1515/coma-2020-0106","DOIUrl":null,"url":null,"abstract":"Abstract Let M be the moduli space of complex Lagrangian submanifolds of a hyperKähler manifold X, and let ω̄ : 𝒜̂ → M be the relative Albanese over M. We prove that 𝒜̂ has a natural holomorphic symplectic structure. The projection ω̄ defines a completely integrable structure on the symplectic manifold 𝒜̂. In particular, the fibers of ω̄ are complex Lagrangians with respect to the symplectic form on 𝒜̂. We also prove analogous results for the relative Picard over M.","PeriodicalId":42393,"journal":{"name":"Complex Manifolds","volume":"7 1","pages":"230 - 240"},"PeriodicalIF":0.5000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/coma-2020-0106","citationCount":"0","resultStr":"{\"title\":\"Complex Lagrangians in a hyperKähler manifold and the relative Albanese\",\"authors\":\"I. Biswas, T. G'omez, André G. Oliveira\",\"doi\":\"10.1515/coma-2020-0106\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Let M be the moduli space of complex Lagrangian submanifolds of a hyperKähler manifold X, and let ω̄ : 𝒜̂ → M be the relative Albanese over M. We prove that 𝒜̂ has a natural holomorphic symplectic structure. The projection ω̄ defines a completely integrable structure on the symplectic manifold 𝒜̂. In particular, the fibers of ω̄ are complex Lagrangians with respect to the symplectic form on 𝒜̂. We also prove analogous results for the relative Picard over M.\",\"PeriodicalId\":42393,\"journal\":{\"name\":\"Complex Manifolds\",\"volume\":\"7 1\",\"pages\":\"230 - 240\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2020-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1515/coma-2020-0106\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Complex Manifolds\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/coma-2020-0106\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Complex Manifolds","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/coma-2020-0106","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

摘要设M为hyperKähler流形X的复拉格朗日子流形的模空间，设ω´:∈→M为M上的相对Albanese，证明了其具有自然全纯辛结构。投影ω定义了辛流形上的一个完全可积结构。特别地，ω的纤维是复拉格朗日量，相对于它的辛形式而言。我们还证明了M上相对皮卡德的类似结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Complex Lagrangians in a hyperKähler manifold and the relative Albanese

Abstract Let M be the moduli space of complex Lagrangian submanifolds of a hyperKähler manifold X, and let ω̄ : 𝒜̂ → M be the relative Albanese over M. We prove that 𝒜̂ has a natural holomorphic symplectic structure. The projection ω̄ defines a completely integrable structure on the symplectic manifold 𝒜̂. In particular, the fibers of ω̄ are complex Lagrangians with respect to the symplectic form on 𝒜̂. We also prove analogous results for the relative Picard over M.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.