Rigid Germs, the Valuative Tree, and Applications to Kato Varieties
Autoren: Ruggiero, Matteo
Vorschau- Presents specific features of the theory of holomorphic dynamics in dimension 2
- Explores 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- Features new, previously unpublished results
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- Über dieses Buch
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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.
- Inhaltsverzeichnis (4 Kapitel)
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Background
Seiten 1-23
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Dynamics in 2D
Seiten 25-78
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Rigid germs in higher dimension
Seiten 79-107
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Construction of non-kahler 3-folds
Seiten 109-161
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Inhaltsverzeichnis (4 Kapitel)
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Bibliografische Information
- Bibliographic Information
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- Buchtitel
- Rigid Germs, the Valuative Tree, and Applications to Kato Varieties
- Autoren
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- Matteo Ruggiero
- Titel der Buchreihe
- Theses (Scuola Normale Superiore)
- Buchreihen Band
- 20
- Copyright
- 2015
- Verlag
- Edizioni della Normale
- Copyright Inhaber
- Scuola Normale Superiore Pisa
- eBook ISBN
- 978-88-7642-559-2
- DOI
- 10.1007/978-88-7642-559-2
- Softcover ISBN
- 978-88-7642-558-5
- Buchreihen ISSN
- 2239-1460
- Auflage
- 1
