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By Jorge Pereira,Luc Pirio

This ebook takes an in-depth examine abelian relatives of codimension one webs within the complicated analytic surroundings. In its classical shape, net geometry is composed within the research of webs as much as neighborhood diffeomorphisms. an important a part of the idea revolves round the suggestion of abelian relation, a specific type of useful relation one of the first integrals of the foliations of an internet. major focuses of the booklet comprise what percentage abelian family can an internet hold and which webs are wearing the maximal attainable variety of abelian kinfolk. The ebook bargains entire proofs of either Chern’s sure and Trépreau’s algebraization theorem, together with all of the precious necessities that transcend straight forward advanced research or uncomplicated algebraic geometry. many of the examples identified brand new 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 is additionally presented.

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An Invitation to Web Geometry (IMPA Monographs) by Jorge Pereira,Luc Pirio

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