{"title":"Théorie des résidus de Leray et formes de Barlet sur une intersection complète singulière","authors":"Aleksandr G. Aleksandrov, Avgust K. Tsikh","doi":"10.1016/S0764-4442(01)02166-8","DOIUrl":null,"url":null,"abstract":"<div><p>Let <em>S</em> be a complex analytic manifold and <em>C</em>⊂<em>S</em> a reduced complete intersection. We construct a complex <span><math><mtext>Ω</mtext><msub><mi></mi><mn>S</mn></msub><msup><mi></mi><mn>•</mn></msup><mtext>(</mtext><mtext>log</mtext><mtext>C)</mtext></math></span> of sheaves of the so-called multi-logarithmic differential forms on <em>S</em> with respect to <em>C</em> and define a residue map <span><math><mtext>res</mtext><mtext>:Ω</mtext><msub><mi></mi><mn>S</mn></msub><msup><mi></mi><mn>•</mn></msup><mtext>(</mtext><mtext>log</mtext><mtext>C)→ω</mtext><msub><mi></mi><mn>C</mn></msub><msup><mi></mi><mn>•</mn></msup></math></span> from this complex onto the Barlet complex <em>ω</em><sub><em>C</em></sub><sup>•</sup> of regular meromorphic differential forms on <em>C</em>. The residue map is proved to be a natural morphism between the two complexes; it follows then that sections of the complex <em>ω</em><sub><em>C</em></sub><sup>•</sup> may be regarded as a generalization of the residue differential forms defined by Leray. Moreover, we show that the map res can be given explicitly in terms of a certain integration current.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 11","pages":"Pages 973-978"},"PeriodicalIF":0.0000,"publicationDate":"2001-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02166-8","citationCount":"24","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0764444201021668","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 24
Abstract
Let S be a complex analytic manifold and C⊂S a reduced complete intersection. We construct a complex of sheaves of the so-called multi-logarithmic differential forms on S with respect to C and define a residue map from this complex onto the Barlet complex ωC• of regular meromorphic differential forms on C. The residue map is proved to be a natural morphism between the two complexes; it follows then that sections of the complex ωC• may be regarded as a generalization of the residue differential forms defined by Leray. Moreover, we show that the map res can be given explicitly in terms of a certain integration current.