An Invitation to Web Geometry - Couverture rigide

Pereira, Jorge Vitorio; Pirio, Luc

Couverture rigide

ISBN 10 : 3319145614 ISBN 13 : 9783319145617

Editeur : Springer International Publishing AG, 2015

Synopsis

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.

A propos du livre

À propos de l'auteur

Jorge Vitorio Pereira is a Research Associate at IMPA (Instituto Nacional de Matematica Pura e Aplicada). Luc Pirio leads research efforts at CNRS.

À propos de la quatrième de couverture

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.

Détails de l'édition

• Éditeur: Springer International Publishing AG
• Date d'édition: 2015
• Langue: anglais
• ISBN 10: 3319145614
• ISBN 13: 9783319145617
• Reliure: Relié
• Nombre de pages: 213
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne