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Foliations with radial Kupka set and pencils of Calabi–Yau hypersurfaces

Published online by Cambridge University Press:  24 November 2006

Omegar Calvo-Andrade ,
Luís Gustavo Mendes  and
Ivan Pan
Omegar Calvo-Andrade
Affiliation:
omegar@agt.uva.es
Luís Gustavo Mendes
Affiliation:
Departamento Matemática, Univ. Federal do Rio Grande do Sul, Av. Bento Gonçalves, 9500, Porto Alegre, CEP 91509-900, Brazilmendes@mat.ufrgs.br
Ivan Pan
Affiliation:
Departamento Matemática, Univ. Federal do Rio Grande do Sul, Av. Bento Gonçalves, 9500, Porto Alegre, CEP 91509-900, Brazilpan@mat.ufrgs.br
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Abstract

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We show that holomorphic singular codimension one foliations of the complex projective space with a Kupka singular set of radial type and verifying some global hypotheses have rational first integral. The generic elements of such pencils are Calabi–Yau.

Keywords

holomorphic foliationfibrationCalabi–Yau manifold37F75 (primary)14D05 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 6 , November 2006 , pp. 1587 - 1593
Copyright
Foundation Compositio Mathematica 2006