Holomorphic Foliations with Singularities : Key Concepts and Modern Results / by Bruno Scárdua.

Format:

Book

Author/Creator:

Scárdua, Bruno, author.

Series:

Latin American Mathematics Series, 2524-6763

Language:

English

Subjects (All):

Geometry, Algebraic.

Dynamics.

Algebraic topology.

Algebraic Geometry.

Dynamical Systems.

Algebraic Topology.

Local Subjects:

Algebraic Geometry.

Dynamical Systems.

Algebraic Topology.

Physical Description:

1 online resource (172 pages)

Edition:

1st ed. 2021.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2021.

Summary:

This concise textbook gathers together key concepts and modern results on the theory of holomorphic foliations with singularities, offering a compelling vision on how the notion of foliation, usually linked to real functions and manifolds, can have an important role in the holomorphic world, as shown by modern results from mathematicians as H. Cartan, K. Oka, T. Nishino, and M. Suzuki. The text starts with a gentle presentation of the classical notion of foliations, advancing to holomorphic foliations and then holomorphic foliations with singularities. The theory behind reduction of singularities is described in detail, as well the cases for dynamics of a local diffeomorphism and foliations on complex projective spaces. A final chapter brings recent questions in the field, as holomorphic flows on Stein spaces and transversely homogeneous holomorphic foliations, along with a list of open questions for further study and research. Selected exercises at the end of each chapter help the reader to grasp the theory. Graduate students in Mathematics with a special interest in the theory of foliations will especially benefit from this book, which can be used as supplementary reading in Singularity Theory courses, and as a resource for independent study on this vibrant field of research.

Contents:

Preface

The Classical Notions of Foliations

Some Results from Several Complex Variables

Holomorphic Foliations: Nonsingular Case

Holomorphic Foliations with Singularities

Holomorphic Foliations Given by Closed 1-Forms

Reduction of Singularities

Holomorphic First Integrals

Dynamics of a Local Diffeomorphism

Foliations on Complex Projective Spaces

Foliations with Algebraic Limit Sets

Some Modern Questions

Miscellaneous exercises and some open questions.

Notes:

Includes bibliographical references and index.

Other Format:

Print version: Scárdua, Bruno Holomorphic Foliations with Singularities

ISBN:

3-030-76705-1

OCLC:

1287103571