关于Frölicher谱序列的退化和小变形

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2018-11-30 DOI:10.1515/coma-2020-0003

Michele Maschio

{"title":"关于Frölicher谱序列的退化和小变形","authors":"Michele Maschio","doi":"10.1515/coma-2020-0003","DOIUrl":null,"url":null,"abstract":"Abstract We study the behavior of the degeneration at the second step of the Frölicher spectral sequence of a 𝒞∞ family of compact complex manifolds. Using techniques from deformation theory and adapting them to pseudo-differential operators we prove a result à la Kodaira-Spencer for the dimension of the second step of the Frölicher spectral sequence and we prove that, under a certain hypothesis, the degeneration at the second step is an open property under small deformations of the complex structure.","PeriodicalId":42393,"journal":{"name":"Complex Manifolds","volume":"7 1","pages":"62 - 72"},"PeriodicalIF":0.5000,"publicationDate":"2018-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/coma-2020-0003","citationCount":"2","resultStr":"{\"title\":\"On the degeneration of the Frölicher spectral sequence and small deformations\",\"authors\":\"Michele Maschio\",\"doi\":\"10.1515/coma-2020-0003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We study the behavior of the degeneration at the second step of the Frölicher spectral sequence of a 𝒞∞ family of compact complex manifolds. Using techniques from deformation theory and adapting them to pseudo-differential operators we prove a result à la Kodaira-Spencer for the dimension of the second step of the Frölicher spectral sequence and we prove that, under a certain hypothesis, the degeneration at the second step is an open property under small deformations of the complex structure.\",\"PeriodicalId\":42393,\"journal\":{\"name\":\"Complex Manifolds\",\"volume\":\"7 1\",\"pages\":\"62 - 72\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2018-11-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1515/coma-2020-0003\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Complex Manifolds\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/coma-2020-0003\",\"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-2020-0003","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: 2

摘要

研究了紧复流形的一种∞族Frölicher谱序列的第二步退化行为。利用变形理论的技术，并将其应用于伪微分算子，证明了Frölicher谱序列第二步维数的一个结果，并证明了在一定的假设下，在复杂结构的小变形下，第二步的退化是开放性质。

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

On the degeneration of the Frölicher spectral sequence and small deformations

Abstract We study the behavior of the degeneration at the second step of the Frölicher spectral sequence of a 𝒞∞ family of compact complex manifolds. Using techniques from deformation theory and adapting them to pseudo-differential operators we prove a result à la Kodaira-Spencer for the dimension of the second step of the Frölicher spectral sequence and we prove that, under a certain hypothesis, the degeneration at the second step is an open property under small deformations of the complex structure.

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.