An Invitation to Web Geometry

• Κύριοι συγγραφείς: Vitório Pereira, Jorge (Συγγραφέας), Pirio, Luc (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Σειρά: IMPA Monographs ; 2
• Θέματα: Mathematics.; Algebraic geometry.; Functions of complex variables.; Differential geometry.; Algebraic Geometry.; Differential Geometry.; Several Complex Variables and Analytic Spaces.

 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. 

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