An invitation to web geometry /
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...
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| Main Authors: | , |
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| Autor Corporativo: | |
| Formato: | livro electrónico |
| Idioma: | English |
| Publicado em: |
Cham
Springer International Publishing Imprint: Springer
2015.
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| Colecção: | IMPA Monographs ;
2 |
| Assuntos: | |
| Acesso em linha: | Click here to view the full text content |
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| Resumo: | 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 webs are carrying the maximal possible number of abelian relations. The book offers complete proofs of both Chern's bound and Trépreau's 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. |
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| Descrição Física: | 1 online resource (xvii, 213 pages) 29 illustrations, 17 illustrations in colour |
| ISBN: | 9783319145624 |