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

Vitório Pereira, Jorge Vitorio

Softcover

ISBN 10: 3319385089 ISBN 13: 9783319385082

Verlag: Springer, 2016

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.

Über diesen Titel

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.

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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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2016
• Sprache: Englisch
• ISBN 10: 3319385089
• ISBN 13: 9783319385082
• Einband: Taschenbuch
• Anzahl der Seiten: 232
• Kontakt zum Hersteller: GPSR Kontakt; ProductSafety@springernature.com; ; Tiergartenstr. 17; Heidelberg; 69121; Deutschland