Description

Book Synopsis

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.



Table of Contents

Introduction.-1.Background.- 2.Dynamics in 2D.- 3.Rigid germs in higher dimension.- 4 Construction of non-Kahler 3-folds.- References.- Index.

Rigid Germs, the Valuative Tree, and Applications

    Product form

    A Paperback / softback by Matteo Ruggiero

    £13.99

    Includes FREE delivery

    Order before 4pm tomorrow for delivery by Tue 15 Sep 2026.

    3 in stock

      Trusted by thousands of customers. See 2,385+ Customer Reviews

      View other formats and editions of Rigid Germs, the Valuative Tree, and Applications by Matteo Ruggiero

      Book details

      Publisher Birkhauser Verlag AG
      Published 29 February 2016
      ISBN-13 9788876425585
      978-8876425585
      ISBN-10 8876425586
      Also in:
      Cybernetics and systems theory Algebraic geometry Algebraic topology

      Description

      Book Synopsis

      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.



      Table of Contents

      Introduction.-1.Background.- 2.Dynamics in 2D.- 3.Rigid germs in higher dimension.- 4 Construction of non-Kahler 3-folds.- References.- Index.

      Recently viewed products

      © 2026 Book Curl

        • American Express
        • Apple Pay
        • Diners Club
        • Discover
        • Google Pay
        • Maestro
        • Mastercard
        • PayPal
        • Shop Pay
        • Union Pay
        • Visa

        Login

        Forgot your password?

        Don't have an account yet?
        Create account