A note on the coSegre class of a subvariety (Q5929543)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A note on the coSegre class of a subvariety |
scientific article; zbMATH DE number 1585216
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the coSegre class of a subvariety |
scientific article; zbMATH DE number 1585216 |
Statements
A note on the coSegre class of a subvariety (English)
0 references
5 April 2001
0 references
coSegre class
0 references
intersection theory
0 references
cotangent bundle
0 references
characteristic cycle
0 references
fundamental cycle
0 references
conic subvariety
0 references
conormal bundle
0 references
Segre class
0 references
Let \(X\) be an algebraic manifold and let \(Z \subset X\) be an irreducible subvariety. Analogously to the construction of the Segre class of Fulton and MacPherson where the normal cone to \(Z\) in \(X\) was used [\textit{W. Fulton}, ``Intersection theory'', Ergeb. Math. Grenzgeb., 3. Folge, Bd. 2 (Berlin 1984; Zbl 0541.14005)] the author introduces the notion of a so-called coSegre class of \((Z,X)\) making use of the closure of the conormal bundle to the nonsingular part of \(Z\) in \(X.\) NEWLINENEWLINENEWLINEAs an application he gives a new proof of a statement (corollary 5) from the paper by \textit{J.-L. Brylinski, A. S. Dubson} and \textit{M. Kashiwara} [C. R. Acad. Sci., Paris, Sér. I 293, 573-576 (1981; Zbl 0492.58021)].
0 references
