Rigid Germs, the Valuative Tree, and Applications to Kato Varieties

• Κύριος συγγραφέας: Ruggiero, Matteo (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Pisa : Scuola Normale Superiore : Imprint: Edizioni della Normale, 2015.
• Σειρά: Publications of the Scuola Normale Superiore ; 20
• Θέματα: Mathematics.; Algebraic geometry.; Dynamics.; Ergodic theory.; Algebraic topology.; Dynamical Systems and Ergodic Theory.; Algebraic Geometry.; Algebraic Topology.

 This thesis deals with specific features of the theory of holomorphic dynamics in dimension 2 and then sets out to study analogous questions in higher dimensions, e.g. dealing with normal forms for rigid germs, and examples of Kato 3-folds. The local dynamics of holomorphic maps around critical points is still not completely understood, in dimension 2 or higher, due to the richness of the geometry of the critical set for all iterates. In dimension 2, the study of the dynamics induced on a suitable functional space (the valuative tree) allows a classification of such maps up to birational conjugacy, reducing the problem to the special class of rigid germs, where the geometry of the critical set is simple. In some cases, from such dynamical data one can construct special compact complex surfaces, called Kato surfaces, related to some conjectures in complex geometry. 

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