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

  • Matteo Ruggiero

Part of the Publications of the Scuola Normale Superiore book series (PSNS, volume 20)

Also part of the Tesi / Theses book sub series (TSNS, volume 20)

Table of contents

  1. Front Matter
    Pages i-xxvi
  2. Matteo Ruggiero
    Pages 1-23
  3. Matteo Ruggiero
    Pages 25-78
  4. Matteo Ruggiero
    Pages 79-107
  5. Matteo Ruggiero
    Pages 109-161
  6. Back Matter
    Pages 163-173

About this book

Introduction

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.

Keywords

local holomorphic dynamics normal forms compact non-Kaehler geometry non-archimedean dynamics compact complex varieties

Authors and affiliations

  • Matteo Ruggiero
    • 1
  1. 1.IMJ - Université Paris DiderotParis Cedex 13France

Bibliographic information