An invitation to web geometry [electronic resource] / Jorge Vitório Pereira, Luc Pirio.

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An invitation to web geometry [electronic resource] / Jorge Vitório Pereira, Luc Pirio.

9783319145624 electronic book
3319145622 electronic book
9783319145617

Cham : Springer, [2015]

©2015

English

1 online resource.

10.1007/978-3-319-14562-4 doi

QA648.5

516.36

This book takes an in-depth look at abelian relations of codimension one webs in the complex analytic setting. In its classical form, web geometry consists in the study of webs up to local diffeomorphisms. A significant part of the theory revolves around the concept of abelian relation, a particular kind of functional relation among the first integrals of the foliations of a web. Two main focuses of the book include how many abelian relations can a web carry and which ℗ℓwebs are carrying the maximal possible number of abelian relations. The book offers complete proofs of both Chernℓ́ℓs bound and Tr©♭preauℓ́ℓs algebraization theorem, including all the necessary prerequisites that go beyond elementary complex analysis or basic algebraic geometry. Most of the examples known up to date of non-algebraizable planar webs of maximal rank are discussed in detail. A historical account of the algebraization problem for maximal rank webs of codimension one is also presented.

Includes bibliographical references and index.

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IMPA monographs ; volume 2.

Print version: 9783319145617

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