Overview
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.
Full Product Details
Author: Jorge Vitório Pereira ,
Luc Pirio
Publisher: Springer International Publishing AG
Imprint: Springer International Publishing AG
Edition: 2015 ed.
Volume: 2
Dimensions:
Width: 15.50cm
, Height: 1.40cm
, Length: 23.50cm
Weight: 5.155kg
ISBN: 9783319145617
ISBN 10: 3319145614
Pages: 213
Publication Date: 23 March 2015
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: Manufactured on demand
We will order this item for you from a manufactured on demand supplier.
Reviews
This book gives an important contribution on the study of web geometry and its relation with algebraic and complex geometry. ... We also note that the book is presented in a self-contained way. ... We remark that several very interesting and different examples are presented and the book moreover illustrates the interplay with several areas of mathematics. (Arturo Fernandez-Perez, Mathematical Reviews, May, 2016) The main aim of the book under review is to present the basic results on this fascinating area of geometry. ... The book is written in a clear and precise style. ... this monograph will be of great interest to graduate students and researchers working in the field of web geometry. (Gabriel Eduard Vilcu, zbMATH 1321.53003, 2015)
The main aim of the book under review is to present the basic results on this fascinating area of geometry. ... The book is written in a clear and precise style. ... this monograph will be of great interest to graduate students and researchers working in the field of web geometry. (Gabriel Eduard Vilcu, zbMATH 1321.53003, 2015)
Author Information
Jorge Vitorio Pereira is a Research Associate at IMPA (Instituto Nacional de Matematica Pura e Aplicada). Luc Pirio leads research efforts at CNRS.
