An Invitation to Web Geometry (Paperback)

Luc Pirio

ISBN 10: 3319385089 / ISBN 13: 9783319385082

Published by Springer International Publishing AG, Cham, 2016

About this Item

Paperback. 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 Cherns bound and Trepreaus 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. This book takes an in-depth look at abelian relations of codimension one webs in the complex analytic setting. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9783319385082

Bibliographic Details

• Title: An Invitation to Web Geometry (Paperback)
• Publisher: Springer International Publishing AG, Cham
• Publication Date: 2016
• Language: English
• ISBN 10: 3319385089
• ISBN 13: 9783319385082
• Binding: Paperback
• Condition: new

About this title

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.

About the Author

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