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An Invitation to Web Geometry (IMPA Monographs, 2, Band 2) - Hardcover

Vitório Pereira, Jorge; Pirio, Luc

 
9783319145617: An Invitation to Web Geometry (IMPA Monographs, 2, Band 2)
Hardcover
ISBN 10: 3319145614 ISBN 13: 9783319145617
Verlag: Springer, 2015

Inhaltsangabe

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.

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Über die Autorin bzw. den Autor

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

Von der hinteren Coverseite

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.

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Verlag
Springer
Erscheinungsdatum
2015
Sprache
Englisch
ISBN 10 
3319145614
ISBN 13 
9783319145617
Einband
Gebundene Ausgabe
Anzahl der Seiten
230
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