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Bounds on leaves one-dimensional foliations.
- Source :
-
Bulletin of the Brazilian Mathematical Society . Apr2003, Vol. 34 Issue 1, p145. 25p. - Publication Year :
- 2003
-
Abstract
- Let X be a variety over an algebraically closed field, η: Ω[sup 1, sub X] → L a one-dimensional singular foliation, and C ⊆ X a projective leaf of η. We prove that 2p[sub a](C) - 2 = deg(LC) + λ(C) - deg(C ∩ S) where p[sub a] (C) is the arithmetic genus, where λ(C) is the co-length in the dualizing sheaf of the subsheaf generated by the Kähler differentials, and where S is the singular locus of η. We bound λ(C) and deg(C ∩ S), and then improve and extend some recent results of Campillo, Carnicer, and de la Fuente, and of du Plessis and Wall. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FOLIATIONS (Mathematics)
*DIFFERENTIAL topology
Subjects
Details
- Language :
- English
- ISSN :
- 16787544
- Volume :
- 34
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Bulletin of the Brazilian Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 10616167
- Full Text :
- https://doi.org/10.1007/s00574-003-0006-3