We consider the question if a five-dimensional manifold can be embedded into a Calabi–Yau manifold of complex dimension 3 such that the real part of the holomorphic volume form induces a given closed 3-form on the 5-manifold. We define an open set of 3-forms in dimension five which we call strongly pseudoconvex, and show that for closed strongly pseudoconvex 3-forms, the perturbative version of this embedding problem can be solved if a finite-dimensional vector space of obstructions vanishes.
{"title":"Closed 3-forms in five dimensions and embedding problems","authors":"Simon Donaldson, Fabian Lehmann","doi":"10.1112/jlms.12897","DOIUrl":"https://doi.org/10.1112/jlms.12897","url":null,"abstract":"<p>We consider the question if a five-dimensional manifold can be embedded into a Calabi–Yau manifold of complex dimension 3 such that the real part of the holomorphic volume form induces a given closed 3-form on the 5-manifold. We define an open set of 3-forms in dimension five which we call strongly pseudoconvex, and show that for closed strongly pseudoconvex 3-forms, the perturbative version of this embedding problem can be solved if a finite-dimensional vector space of obstructions vanishes.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12897","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140351624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}