Birational Geometry of Foliations

• Main Author: Brunella, Marco (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Series: IMPA Monographs ; 1
• Subjects: Mathematics.; Geometry.; Hyperbolic geometry.; Number theory.; Hyperbolic Geometry.; Number Theory.

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.

Table 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.