Pull-back components of the space of holomorphic foliations on CP(n), n >=3

Authors
Cerveau, D Neto, AL Edixhoven, SJ
Citation
D. Cerveau et al., Pull-back components of the space of holomorphic foliations on CP(n), n >=3, J ALGEBR GE, 10(4), 2001, pp. 695-711
Citations number
14
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF ALGEBRAIC GEOMETRY
ISSN journal
10563911 → ACNP
Volume
10
Issue
4
Year of publication
2001
Pages
695 - 711
Database
ISI
SICI code
1056-3911(200110)10:4<695:PCOTSO>2.0.ZU;2-T
Abstract
Let F(k; n) be the space of codimension-one holomorphic foliations of degre e k on CP(n). In this paper we prove that, if n greater than or equal to 3, then the set of foliations F of CP(n), which can be written as F = F* (G), where G is a foliation of degree d in CP(2) and F: CP(n) --> CF(2) is a ge neric rational map of degree nu, is an irreducible component of the space F ((d + 2)nu - 2; n).