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Planar web geometry through abelian relations and singularities. (English) Zbl 1133.53012

Griffiths, Phillip A. (ed.), Inspired by S. S. Chern. A memorial volume in honor of a great mathematician. Hackensack, NJ: World Scientific (ISBN 978-981-270-061-2/hbk; 978-981-270-062-9/pbk). Nankai Tracts in Mathematics 11, 269-295 (2006).
This paper is the Chapter 10 of a volume in honour of S. S. Chern. The author presents basic and new results on webs consisting of \(d \geq 1\) complex analytic foliations of curves in general position of the projective plane. To illustrate methods and open problems, introductory examples are given. The paper has three sections. In the first one, one can see an acknowledgement to the work of Chern and Blaschke and the introduction of the main objects treated in the paper. The second section essentially deals with the geometric study of planar webs with the help of certain generically finite morphisms and a not necessarily integrable connection associated to the web where possible horizontal sections are identified with the space of abelian relations, The paper ends with a singular approach for planar webs.
For the entire collection see [Zbl 1105.00006].

MSC:

53A60 Differential geometry of webs
14C21 Pencils, nets, webs in algebraic geometry
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