Foliation Theory in Algebraic Geometry

  • Paolo Cascini
  • James McKernan
  • Jorge Vitório Pereira
Part of the Simons Symposia book series (SISY)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Carolina Araujo, Stéphane Druel
    Pages 1-20
  3. Fedor Bogomolov, Michael McQuillan
    Pages 21-51
  4. Fedor Bogomolov, Bruno De Oliveira
    Pages 53-71
  5. Stefan Kebekus, Thomas Peternell
    Pages 73-102
  6. Paolo Cascini, James McKernan, Jorge Vitório Pereira
    Pages E1-E2

About these proceedings

Introduction

Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013. 

Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classification of psuedoeffective codimension one distributions.

Foliations play a fundamental role in algebraic geometry, for example in the proof of abundance for threefolds and to a solution of the Green-Griffiths conjecture for surfaces of general type with positive Segre class. The purpose of this volume is to foster communication and enable interactions between experts who work on holomorphic foliations and birational geomet
ry, and to bring together leading researchers to demonstrate the powerful connection of ideas, methods, and goals shared by these two areas of study.

Keywords

Algebraic Geometry Canonical Singularities Foliation Projective Manifolds Rational Curves

Editors and affiliations

  • Paolo Cascini
    • 1
  • James McKernan
    • 2
  • Jorge Vitório Pereira
    • 3
  1. 1.Mathematics DepartmentImperial College of LondonLondonUK
  2. 2.Department of MathematicsUC San DiegoLa JollaUSA
  3. 3.IMPARio de JaneiroBrazil

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-24460-0
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-24458-7
  • Online ISBN 978-3-319-24460-0
  • Series Print ISSN 2365-9564
  • Series Online ISSN 2365-9572
  • About this book