Rigid Germs, the Valuative Tree, and Applications to Kato Varieties
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Beschreibung
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.
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higher dimensions Contains a detailed study of an example of a non-Kahler 3-fold of type Kato Features new, previously unpublished results
Autor*in
Matteo Ruggiero
Themen in »Rigid Germs, the Valuative Tree, and Applications to Kato Varieties«
local holomorphic dynamics normal forms compact non-Kaehler geometry non-archimedean dynamics compact complex varieties