An Invitation to Web Geometry - Couverture rigide

Vitório Pereira, Jorge; 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.

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: 230
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Allemagne