Hundreds of Mathematics books at half price + FREE shipping! Get yours now >>

IMPA Monographs

An Invitation to Web Geometry

Authors: Pereira, Jorge Vitorio, Pirio, Luc

  • I​ncludes a short survey of the history of the field
  • Presentation is elementary and clear
  • Allows the reader to have a global picture of what were and what are the main questions of the field
see more benefits

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-319-14562-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-319-14561-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: November 17, 2016
  • ISBN 978-3-319-38508-2
  • Free shipping for individuals worldwide
About this book

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 authors

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

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 Fernández-Pérez, 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)


Table of contents (6 chapters)

  • Local and Global Webs

    Pereira, Jorge Vitório (et al.)

    Pages 1-37

  • Abelian Relations

    Pereira, Jorge Vitório (et al.)

    Pages 39-64

  • Abel’s Addition Theorem

    Pereira, Jorge Vitório (et al.)

    Pages 65-90

  • The Converse to Abel’s Theorem

    Pereira, Jorge Vitório (et al.)

    Pages 91-114

  • Algebraization of Maximal Rank Webs

    Pereira, Jorge Vitório (et al.)

    Pages 115-149

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-319-14562-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-319-14561-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: November 17, 2016
  • ISBN 978-3-319-38508-2
  • Free shipping for individuals worldwide
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
An Invitation to Web Geometry
Authors
Series Title
IMPA Monographs
Series Volume
2
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-14562-4
DOI
10.1007/978-3-319-14562-4
Hardcover ISBN
978-3-319-14561-7
Softcover ISBN
978-3-319-38508-2
Edition Number
1
Number of Pages
XVII, 213
Number of Illustrations and Tables
12 b/w illustrations, 17 illustrations in colour
Topics