An Invitation to Web Geometry

Softcover Nachdruck of the original 1. Auflage 2015
ISBN: 978-3-319-38508-2
Verlag: Springer International Publishing

Buch, Englisch, Band 2, 213 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 3999 g

Reihe: IMPA Monographs

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.

Zielgruppe

Research

Autoren/Hrsg.

Pirio, Luc

Vitório Pereira, Jorge

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Mathematische Analysis

Inhaltsverzeichnis

Local and Global Webs.- Abelian Relations.- Abel's Addition Theorem.- The Converse to Abel's Theorem.- Algebraization.- Exceptional Webs.    

Über Autor(innen)

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