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Foliation Theory in Algebraic Geometry by Paolo Cascini, James McKernan, Jorge Pereira
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**About this book :- **
**Foliation Theory in Algebraic Geometry** written by
** Paolo Cascini, James McKernan, Jorge Pereira **

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 geometry, and to bring together leading researchers to demonstrate the powerful connection of ideas, methods, and goals shared by these two areas of study.

**Book Detail :- **
** Title: ** Foliation Theory in Algebraic Geometry
** Edition: **
** Author(s): ** Paolo Cascini, James McKernan, Jorge Pereira
** Publisher: ** Springer International Publishing
** Series: ** Simons Symposia
** Year: ** 2016
** Pages: ** 221
** Type: ** PDF
** Language: ** English
** ISBN: ** 978-3-319-24458-7, 978-3-319-24460-0
** Country: ** US
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**About Author :- **

The author ** James McKernan **** (born 1964) is a mathematician, and a professor of mathematics at the University of California, San Diego. He was a professor at MIT from 2007 until 2013.
McKernan was educated at the Campion School, Hornchurch, and Trinity College, Cambridge, before going on to earn his Ph.D. from Harvard University in 1991. His dissertation, On the Hyperplane Sections of a Variety in Projective Space, was supervised by Joe Harris.
McKernan was the joint winner of the Cole Prize in 2009, and joint recipient of the Clay Research Award in 2007. Both honors were received jointly with his colleague Christopher Hacon. He gave an invited talk at the International Congress of Mathematicians in 2010, on the topic of "Algebraic Geometry". He was the joint winner (with Christopher Hacon) of the 2018 Breakthrough Prize in Mathematics.
He was elected as a Fellow of the American Mathematical Society in the 2020 Class, for "contributions to algebraic geometry, in particular his proof of the finite generation of the canonical ring, the existence of flips and the boundedness of varieties of log general type".[7
**

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**Book Contents :- **
**Foliation Theory in Algebraic Geometry** written by
** Paolo Cascini, James McKernan, Jorge Pereira **
cover the following topics.

On Fano Foliations by Carolina Araujo and Stéphane Druel

Rational Curves on Foliated Varieties by Fedor Bogomolov and Michael McQuillan

Local Structure of Closed Symmetric 2-Differentials by Fedor Bogomolov and Bruno De Oliveira

Aspects of the Geometry of Varieties with Canonical Singularities by Stefan Kebekus and Thomas Peternell

Geometric Structures and Substructures on Uniruled Projective Manifolds by Ngaiming Mok Foliations, Shimura Varieties, and the Green-Griffiths-Lang

Conjecture by Erwan Rousseau

On the Structure of Codimension 1 Foliations with Pseudoeffective Conormal Bundle by Frédéric Touzet

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