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An Invitation to Web Geometry

  • Jorge Vitório Pereira
  • Luc Pirio

Part of the IMPA Monographs book series (IMPA, volume 2)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Jorge Vitório Pereira, Luc Pirio
    Pages 1-37
  3. Jorge Vitório Pereira, Luc Pirio
    Pages 39-64
  4. Jorge Vitório Pereira, Luc Pirio
    Pages 65-90
  5. Jorge Vitório Pereira, Luc Pirio
    Pages 91-114
  6. Jorge Vitório Pereira, Luc Pirio
    Pages 115-149
  7. Jorge Vitório Pereira, Luc Pirio
    Pages 151-194
  8. Back Matter
    Pages 195-213

About this book

Introduction

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.

Keywords

Abelian relations Abel’s addition Theorem Conormals of webs of maximal rank Global webs Planar 3-webs

Authors and affiliations

  • Jorge Vitório Pereira
    • 1
  • Luc Pirio
    • 2
  1. 1.Instituto de Matemática Pura e AplicadaRio de JaneiroBrazil
  2. 2.UMR 6625 – CNRSInstitut de Recherches Mathématiques de RennesRennesFrance

Bibliographic information