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Holomorphic vector fields transverse to polydiscs
Author(s) -
Bracci Filippo,
Scárdua Bruno
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdl005
Subject(s) - holomorphic function , foliation (geology) , codimension , injective function , polydisc , boundary (topology) , transversality , mathematics , pure mathematics , transverse plane , mathematical analysis , geometry , geology , structural engineering , engineering , geochemistry , metamorphic rock
In this article, we study holomorphic vector fields transverse to the boundary of a polydisc in ℂ n , n ⩾ 3. We prove that, under a suitable hypothesis of transversality with the boundary of the polydisc, the foliation is the pull‐back of a linear hyperbolic foliation via a locally injective holomorphic map. This is the n ⩾ 3 version for one‐dimensional foliations of a previous result proved for n = 2 by Brunella and Sad and for codimension‐one foliations by Ito and Scárdua.