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

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

    Posted By: step778
    Date: 13 May 2022 08:54:58
    Rigid Germs, the Valuative Tree, and Applications to Kato Varieties

    Matteo Ruggiero, "Rigid Germs, the Valuative Tree, and Applications to Kato Varieties"
    English | 2016 | pages: 194 | ISBN: 8876425586 | PDF | 1,1 mb

    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.

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