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Rigid germs, the valuative tree, and...

Ruggiero, Matteo.

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Rigid germs, the valuative tree, and applications to Kato varieties

Record Type:	Electronic resources : Monograph/item
Title/Author:	Rigid germs, the valuative tree, and applications to Kato varieties/ by Matteo Ruggiero.
Author:	Ruggiero, Matteo.
Published:	Pisa :Scuola Normale Superiore : : 2015.,
Description:	xxvi, 173 p. :ill., digital ;24 cm.
[NT 15003449]:	Introduction.-1.Background -- 2.Dynamics in 2D -- 3.Rigid germs in higher dimension -- 4 Construction of non-Kahler 3-folds -- References -- Index.
Contained By:	Springer eBooks
Subject:	Holomorphic functions. -
Online resource:	http://dx.doi.org/10.1007/978-88-7642-559-2
ISBN:	9788876425592$q(electronic bk.)

Rigid germs, the valuative tree, and applications to Kato varieties
Ruggiero, Matteo.

Rigid germs, the valuative tree, and applications to Kato varieties[electronic resource] /by Matteo Ruggiero. - Pisa :Scuola Normale Superiore :2015. - xxvi, 173 p. :ill., digital ;24 cm. - Tesi ;20. - Tesi ;20..

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

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.

ISBN: 9788876425592$q(electronic bk.)

Standard No.: 10.1007/978-88-7642-559-2doiSubjects--Topical Terms:

700319
Holomorphic functions.

LC Class. No.: QA331

Dewey Class. No.: 515.98

Rigid germs, the valuative tree, and applications to Kato varieties
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505 0 $a Introduction.-1.Background -- 2.Dynamics in 2D -- 3.Rigid germs in higher dimension -- 4 Construction of non-Kahler 3-folds -- References -- Index.
520 $a 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.
650 0 $a Holomorphic functions. $3 700319
650 0 $a Germs (Mathematics) $3 2165844
650 1 4 $a Mathematics. $3 515831
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650 2 4 $a Algebraic Geometry. $3 893861
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