Theses (Scuola Normale Superiore)

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

Authors: Ruggiero, Matteo

  • 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  • Features new, previously unpublished results
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eBook 11,89 €
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Softcover 18,72 €
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  • ISBN 978-88-7642-558-5
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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.

Buy this book

eBook 11,89 €
price for Spain (gross)
  • ISBN 978-88-7642-559-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 18,72 €
price for Spain (gross)
  • ISBN 978-88-7642-558-5
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Rigid Germs, the Valuative Tree, and Applications to Kato Varieties
Authors
Series Title
Theses (Scuola Normale Superiore)
Series Volume
20
Copyright
2015
Publisher
Edizioni della Normale
Copyright Holder
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
Series ISSN
2239-1460
Edition Number
1
Topics