By Jorge Pereira,Luc Pirio

This booklet takes an in-depth examine abelian kin of codimension one webs within the complicated analytic environment. In its classical shape, net geometry is composed within the examine of webs as much as neighborhood diffeomorphisms. an important a part of the idea revolves round the notion of abelian relation, a specific form of useful relation one of the first integrals of the foliations of an internet. major focuses of the e-book comprise what percentage abelian family members can an online hold and which webs are sporting the maximal attainable variety of abelian kin. The booklet deals entire proofs of either Chern’s sure and Trépreau’s algebraization theorem, together with the entire beneficial must haves that transcend easy advanced research or uncomplicated algebraic geometry. many of the examples recognized modern of non-algebraizable planar webs of maximal rank are mentioned intimately. A old account of the algebraization challenge for maximal rank webs of codimension one can also be presented.

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