Rigid germs, the valuative tree, and applications to Kato varieties / Matteo Ruggiero

• Record Nr.: UNICAMPANIAVAN00114031
• Autore: Ruggiero, Matteo
• Pubbl/distr/stampa: Pisa, : Edizioni della Normale, 2015
• Titolo uniforme: Rigid germs, the valuative tree, and applications to Kato varieties
• Descrizione fisica: XXVI, 173 p. : ill. ; 24 cm
• Soggetti: 14J17 - Singularities of surfaces or higher-dimensional varieties [MSC 2020]; 30D05 - Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable [MSC 2020]; 32-XX - Several complex variables and analytic spaces [MSC 2020]; 32H50 - Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables [MSC 2020]; 32S25 - Complex surface and hypersurface singularities [MSC 2020]; 37F25 - Renormalization of holomorphic dynamical systems [MSC 2020]
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Tesi di dottorato in Matematica
• Nota di contenuto: 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.