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Rigid Germs, the Valuative Tree, and Applications to Kato Varieties: Publications of the Scuola Normale Superiore, cartea 20

Autor Matteo Ruggiero
en Limba Engleză Paperback – 29 feb 2016
This thesis deals with specific featuresof the theory of holomorphic dynamics in dimension 2 and then sets out to studyanalogous questions in higher dimensions, e.g. dealing with normal forms forrigid germs, and examples of Kato 3-folds.
The local dynamics of holomorphic mapsaround critical points is still not completely understood, in dimension 2 orhigher, due to the richness of the geometry of the critical set for alliterates.
In dimension 2, the study of thedynamics induced on a suitable functional space (the valuative tree) allows aclassification of such maps up to birational conjugacy, reducing the problem tothe special class of rigid germs, where the geometry of the critical set issimple.
In some cases, from such dynamical dataone can construct special compact complex surfaces, called Kato surfaces,related to some conjectures in complex geometry.
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Specificații

ISBN-13: 9788876425585
ISBN-10: 8876425586
Pagini: 200
Ilustrații: Approx. 200 p.
Dimensiuni: 150 x 240 x 15 mm
Greutate: 0.41 kg
Ediția:1st ed. 2016
Editura: Scuola Normale Superiore
Colecția Edizioni della Normale
Seriile Publications of the Scuola Normale Superiore, Theses (Scuola Normale Superiore)

Locul publicării:Pisa, Switzerland

Cuprins

Introduction.-1.Background.-2.Dynamics in 2D.- 3.Rigid germs in higher dimension.- 4 Construction ofnon-Kahler 3-folds.- References.- Index.

Caracteristici

specific features of the theory of holomorphic dynamics in dimension 2 analogous questions in higher dimensions Contains adetailed study of an example of a non-Kahler 3-fold of type Kato Featuresnew, previously unpublished results