File  
language 
eng

Author 
Fukuma Yoshiaki
Matsunaga, Hiromichi
Shoji, Kunitaka

Description  Let M be a complex projective manifold. We say that M has a foliation by curves if there exists a line bundle L on M and a nonzero homomorphism i : L → T_M, where T_M is a tangent bundle of M. If the above homomorphism L → T_M is injective, then we say that a foliation is nonsingular. Let L_α be a 1dimensional connected manifold. Then we say that L_α is a leaf of foliation i : L → TM if M = ∪_αL_α, L_α∩L_β =(0+/) for α≠β, and for x ∈L_α i(L)_x is a tangent bundle of L_α at x. In this paper we consider the case in which M is a projective surface. We use a notation S instead of M.
If S is a ruled surface, that is, there exists a surjective morphism with connected fibers π : S → C such that any general fiber of π is P^1, where C is a smooth projective curve, then the foliations by curves on S have been studied by GomezMont ([GM II]). Here we consider the case in which there exists a surjective morphism π : S → C with connected fibers such that any general fiber is an elliptic curve. We call this surface an elliptic surface over a smooth projective curve. Here we note that elliptic surfaces may have singular fibers and all types of singular fibers have been classified by Kodaira. This paper consists of the following three parts; (1) examples of special type of foliations on ellitpic surfaces, (2) a family of foliations on elliptic surfaces, (3) the existence of elliptic surfaces which have foliations. In [B], Brunella obtained some interesting results for foliations without singularities on nonsingular algebraic surfaces, and pointed out that a turbulent foliation can appear (un feuilletage tourbillonne). Here we mean by a foliation a holomorphic one, and discuss foliations on elliptic surfaces. 
Subject  Holomorphic Foliation
Elliptic Surface

Journal Title 
島根大学総合理工学部紀要. シリーズB

Volume  36

Start Page  11

End Page  19

ISSN  13427121

Published Date  200303

NCID  AA11157123

Publisher  島根大学総合理工学部

NII Type 
Departmental Bulletin Paper

Format 
PDF

Text Version 
出版社版

Gyoseki ID  e17826

OAIPMH Set 
Interdisciplinary Graduate School of Science and Engineering
