Birational Geometry of Foliations

The text presents the birational classification of holomorphic foliations of surfaces. It discusses at length the theory developed by L.G. Mendes, M. McQuillan and the author to study foliations of surfaces in the spirit of the classification of complex algebraic surfaces.

List of contents

Introduction: From Surfaces to Foliations.- Local Theory.- Foliations and Line Bundles.- Index Theorems.- Some Special Foliations.- Minimal Models.- Global 1-forms and Vector Fields.- The Rationality Criterion.- Numerical Kodaira Dimension.- Kodaira Dimension.- References.

About the author

Marco Brunella was a CNRS researcher working at Institut de Mathematiques de Bourgogne in Dijon, France. He has produced extraordinary mathematical work, focusing on the study of Holomorphic Foliations and Complex Geometry. Dr. Brunella passed away in January 2012, but his profound, creative mathematics continues to have an impact on geometers and analysts.

Summary

The text presents the birational classification of holomorphic foliations of surfaces.  It discusses at length the theory developed by L.G. Mendes, M. McQuillan and the author to study foliations of surfaces  in the spirit of the classification of complex algebraic surfaces.

Product details

• Authors: Marco Brunella
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2016
• EAN: 9783319365657
• ISBN: 978-3-31-936565-7
• No. of pages: 130
• Dimensions: 155 mm x 235 mm x 8 mm
• Weight: 235 g
• Illustrations: XIV, 130 p. 35 illus.
• Series: IMPA Monographs; IMPA Monographs
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Geometry; Zahlentheorie, Geometrie, B, geometry, Mathematics and Statistics, Number Theory, Hyperbolic Geometry, The Rationality Criterion