Overview
- specific features of the theory of holomorphic dynamics in dimension 2
- analogous questions in higher dimensions
- Contains a detailed study of an example of a non-Kahler 3-fold of type Kato
- Features new, previously unpublished results
Part of the book series: Publications of the Scuola Normale Superiore (PSNS, volume 20)
Part of the book sub series: Theses (Scuola Normale Superiore) (TSNS)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (4 chapters)
-
Front Matter
-
Back Matter
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Rigid Germs, the Valuative Tree, and Applications to Kato Varieties
Authors: Matteo Ruggiero
Series Title: Publications of the Scuola Normale Superiore
DOI: https://doi.org/10.1007/978-88-7642-559-2
Publisher: Edizioni della Normale Pisa
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Scuola Normale Superiore Pisa 2015
Softcover ISBN: 978-88-7642-558-5Published: 29 February 2016
eBook ISBN: 978-88-7642-559-2Published: 28 April 2016
Series ISSN: 2239-1460
Series E-ISSN: 2532-1668
Edition Number: 1
Topics: Dynamical Systems and Ergodic Theory, Algebraic Geometry, Algebraic Topology