NDLI: Bounds on leaves of one-dimensional foliations

Content Provider	Springer Nature Link
Author	Esteves, E. Kleiman, S.
Copyright Year	2003
Abstract	Let X be a variety over an algebraically closed field, $$ \eta :\Omega ^{1}_{X} \to {\cal L} $$ a onedimensional singular foliation, and $$ C \subseteq X $$ a projective leaf of η. We prove that $$ 2p_{a} {\left( C \right)} - 2 = \deg {\left( {{\cal L}\left\| C \right.} \right)} + \lambda {\left( C \right)} - \deg {\left( {C \cap S} \right)} $$ where p a (C) is the arithmetic genus, where λ(C) is the colength 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 $$ \deg {\left( {C \cap S} \right)} $$ , and then improve and extend some recent results of Campillo, Carnicer, and de la Fuente, and of du Plessis and Wall.
Starting Page	145
Ending Page	169
Page Count	25
File Format	PDF
ISSN	16787544
Journal	Bulletin of the Brazilian Mathematical Society
Volume Number	34
Issue Number	1
e-ISSN	16787714
Language	English
Publisher	Springer-Verlag
Publisher Date	2003-01-01
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	foliations curves singularities
Content Type	Text
Resource Type	Article
Subject	Mathematics

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Bounds on leaves of one-dimensional foliations