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

By Jorge Pereira,Luc Pirio

This booklet takes an in-depth examine abelian relatives of codimension one webs within the advanced analytic surroundings. In its classical shape, internet geometry is composed within the examine of webs as much as neighborhood diffeomorphisms. an important a part of the idea revolves round the idea of abelian relation, a selected form of practical relation one of the first integrals of the foliations of an internet. major focuses of the booklet contain what percentage abelian kinfolk can an internet hold and which webs are wearing the maximal attainable variety of abelian kinfolk. The ebook deals whole proofs of either Chern’s sure and Trépreau’s algebraization theorem, together with all of the precious must haves that transcend straight forward complicated research or simple algebraic geometry. lots of the examples identified 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 is additionally presented.

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