{"title":"Real Submanifolds of \\(\\mathbf{C}^2\\) With Singularities","authors":"V. K. Beloshapka","doi":"10.1134/S1061920823030020","DOIUrl":null,"url":null,"abstract":"<p> We consider real submanifolds of <span>\\(\\mathbf{C}^2\\)</span> with singularities of three types: <span>\\(RC\\)</span>-singular 2 - dimensional surfaces, real quadratic cones, and hypersurfaces with degeneration of the Levi form. The holomorphic automorphisms of singular germs are evaluated. We also discuss resolution of singularities in the context of <span>\\(\\mathit{CR}\\)</span> geometry. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 3","pages":"280 - 293"},"PeriodicalIF":1.7000,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1061920823030020","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We consider real submanifolds of \(\mathbf{C}^2\) with singularities of three types: \(RC\)-singular 2 - dimensional surfaces, real quadratic cones, and hypersurfaces with degeneration of the Levi form. The holomorphic automorphisms of singular germs are evaluated. We also discuss resolution of singularities in the context of \(\mathit{CR}\) geometry.
期刊介绍：
Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.
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