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An invitation to web geometry

Pereira, Jorge Vitorio.

An invitation to web geometry

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	An invitation to web geometryby Jorge Vitorio Pereira, Luc Pirio.
作者:	Pereira, Jorge Vitorio.
其他作者:	Pirio, Luc.
出版者:	Cham :Springer International Publishing :2015.
面頁冊數:	xvii, 213 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Webs (Differential geometry)
電子資源:	http://dx.doi.org/10.1007/978-3-319-14562-4
ISBN:	9783319145624 (electronic bk.)

An invitation to web geometry
Pereira, Jorge Vitorio.

An invitation to web geometry[electronic resource] /by Jorge Vitorio Pereira, Luc Pirio. - Cham :Springer International Publishing :2015. - xvii, 213 p. :ill., digital ;24 cm. - IMPA monographs ;v.2. - IMPA monographs ;v.2..

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

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 Trepreau'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.

ISBN: 9783319145624 (electronic bk.)

Standard No.: 10.1007/978-3-319-14562-4doiSubjects--Topical Terms:

208691
Webs (Differential geometry)

LC Class. No.: QA648.5

Dewey Class. No.: 516.36

An invitation to web geometry
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505 0 $a Local and Global Webs -- Abelian Relations -- Abel's Addition Theorem -- The Converse to Abel's Theorem -- Algebraization -- Exceptional Webs.
520 $a 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 Trepreau'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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