Rigid Germs, the Valuative Tree, and Applications to Kato by Matteo Ruggiero

By Matteo Ruggiero

This thesis bargains with particular features
of the idea of holomorphic dynamics in size 2 after which units out to study
analogous questions in greater dimensions, e.g. facing general types for
rigid germs, and examples of Kato 3-folds.

The neighborhood dynamics of holomorphic maps
around serious issues continues to be no longer thoroughly understood, in measurement 2 or
higher, end result of the richness of the geometry of the severe set for all
iterates.

In measurement 2, the research of the
dynamics triggered on an appropriate practical area (the valuative tree) permits a
classification of such maps as much as birational conjugacy, decreasing the matter to
the specified type of inflexible germs, the place the geometry of the serious set is
simple.

In a few situations, from such dynamical data
one can build designated compact advanced surfaces, referred to as Kato surfaces,
related to a couple conjectures in complicated geometry.

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