{"title":"Vector bundles on real abelian varieties","authors":"Archana S. Morye","doi":"10.1016/j.difgeo.2023.102077","DOIUrl":null,"url":null,"abstract":"<div><p>This paper is about real holomorphic vector bundles<span> on real abelian varieties. The main result of the paper gives several conditions that are necessary and sufficient for the existence of a holomorphic connection on a real holomorphic vector bundle over a real abelian variety. Also proved is an analogue, for real abelian varieties, of a result of Simpson, which gives a criterion for a holomorphic vector bundle to arise by successive extensions of stable vector bundles with vanishing Chern classes.</span></p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"91 ","pages":"Article 102077"},"PeriodicalIF":0.6000,"publicationDate":"2023-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Geometry and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0926224523001031","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
This paper is about real holomorphic vector bundles on real abelian varieties. The main result of the paper gives several conditions that are necessary and sufficient for the existence of a holomorphic connection on a real holomorphic vector bundle over a real abelian variety. Also proved is an analogue, for real abelian varieties, of a result of Simpson, which gives a criterion for a holomorphic vector bundle to arise by successive extensions of stable vector bundles with vanishing Chern classes.
期刊介绍：
Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.
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