{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1363388844369883264.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.1142/s0129167x98000324"}},{"identifier":{"@type":"URI","@value":"https://www.worldscientific.com/doi/pdf/10.1142/S0129167X98000324"}},{"identifier":{"@type":"NAID","@value":"30010697402"}}],"dc:title":[{"@value":"AN ADJUNCTION FORMULA FOR LOCAL COMPLETE INTERSECTIONS"}],"description":[{"notation":[{"@value":"In this article, we study various kinds of indices of a vector field on a singular variety and as an application, we prove, for a compact \"strong\" local complete intersection V with isolated singularities, a formula expressing the Euler-Poincare characteristic x (^ ) 0 I ^ i n terms of the top Chern class of the virtual tangent bundle of V and the Milnor numbers of the singularities (Theorem 2.4). For a vector field t i o n a singular variety V, we consider the \"Schwartz index\", the \"GSV-index\" and the \"virtual index\" at the singularity of v. All these reduce to the usual Poincare-Hopf index when the singularity of v is in the regular part of V, so we compare them when it is in the singular part of V. M.-H. Schwartz defined an index for \"radial\" vector fields on a singular variety V, see [21, 4]. When the singularities of V are isolated, as they are in this article, this definition can be easily extended to vector fields which are not radial. We do this in Sec. 1 below and we call the corresponding index the Schwartz index of a vector field. We show that, for a global vector field with isolated singularities on a compact variety V, the sum of the Schwartz indices gives x(V) (Theorem 1.2). In [12] there is a definition of a local index for stratified vector fields on singular varieties, extending Schwartz' definition for radial vector fields. Presumably our definition of the Schwartz index coincides with that in [12]. We then recall the GSV-index, which is defined in [22, 9, 23]. It is defined for a vector field on a local complete intersection V in a complex manifold M and it"}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1383388844369883264","@type":"Researcher","foaf:name":[{"@value":"JOSÉ SEADE"}],"jpcoar:affiliationName":[{"@value":"Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, Circuito Exterior, México 04510 D.F., México"}]},{"@id":"https://cir.nii.ac.jp/crid/1383388844369883265","@type":"Researcher","foaf:name":[{"@value":"TATSUO SUWA"}],"jpcoar:affiliationName":[{"@value":"Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"0129167X"},{"@type":"EISSN","@value":"17936519"},{"@type":"NCID","@value":"AA10754794"}],"prism:publicationName":[{"@value":"International Journal of Mathematics"}],"dc:publisher":[{"@value":"World Scientific Pub Co Pte Lt"}],"prism:publicationDate":"1998-09","prism:volume":"09","prism:number":"06","prism:startingPage":"759","prism:endingPage":"768"},"reviewed":"false","url":[{"@id":"https://www.worldscientific.com/doi/pdf/10.1142/S0129167X98000324"}],"createdAt":"2002-07-27","modifiedAt":"2019-08-06","relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1360584339749408640","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Motivic Hirzebruch Class and Related Topics"}]},{"@id":"https://cir.nii.ac.jp/crid/1360848656877133568","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Hirzebruch–Milnor classes of complete intersections"}]},{"@id":"https://cir.nii.ac.jp/crid/1390001205065723392","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isCitedBy"],"jpcoar:relatedTitle":[{"@value":"特異多様体の特性類"},{"@language":"ja-Kana","@value":"トクイ タヨウタイ ノ トクセイルイ"}]}],"dataSourceIdentifier":[{"@type":"CROSSREF","@value":"10.1142/s0129167x98000324"},{"@type":"CIA","@value":"30010697402"},{"@type":"OPENAIRE","@value":"doi_dedup___::375952bee873e148272597e76806939e"},{"@type":"CROSSREF","@value":"10.1016/j.aim.2013.04.001_references_DOI_B6m9mEUQ3bFYilQX4vCZPHLnzMt"},{"@type":"CROSSREF","@value":"10.1007/978-3-031-31925-9_6_references_DOI_B6m9mEUQ3bFYilQX4vCZPHLnzMt"}]}