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Automorphisms in Birational and Affine Geometry by Ivan Cheltsov, Ciro Ciliberto, Hubert Flenner, James McKernan
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**About this book :- **
**Automorphisms in Birational and Affine Geometry** written by
** Ivan Cheltsov, Ciro Ciliberto, Hubert Flenner, James McKernan **

The main focus of this text volume is on the problem of describing the automorphism groups of affine and projective varieties, a classical subject in algebraic geometry where, in both cases, the automorphism group is often infinite dimensional. The collection covers a wide range of topics and is intended for researchers in the fields of classical algebraic geometry and birational geometry (Cremona groups) as well as affine geometry with an emphasis on algebraic group actions and automorphism groups. It presents original research and surveys and provides a valuable overview of the current state of the art in these topics.

Bringing together specialists from projective, birational algebraic geometry and affine and complex algebraic geometry, including Mori theory and algebraic group actions, this book is the result of ensuing talks and discussions from the conference “Groups of Automorphisms in Birational and Affine Geometry” held in October 2012, at the CIRM, Levico Terme, Italy. The talks at the conference highlighted the close connections between the above-mentioned areas and promoted the exchange of knowledge and methods from adjacent fields. The topics in affine geometry include: different aspects of the automorphism groups of affine varieties, flexibility properties in affine algebraic and analytic geometry, automorphisms of affine spaces and Shestakov–Umirbaev theory, affine geometry in positive characteristic, the automorphism groups of configuration spaces and other classes of affine varieties and deformations of certain group actions on affine varieties.

**Book Detail :- **
** Title: ** Automorphisms in Birational and Affine Geometry: Levico Terme, Italy, October 2012
** Edition: **
** Author(s): ** Ivan Cheltsov, Ciro Ciliberto, Hubert Flenner, James McKernan
** Publisher: ** Springer International Publishing
** Series: ** Springer Proceedings in Mathematics & Statistics 79
** Year: ** 2014
** Pages: ** 509
** Type: ** PDF
** Language: ** English
** ISBN: ** 978-3-319-05680-7,978-3-319-05681-4
** 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 :- **
**Automorphisms in Birational and Affine Geometry** written by
** Ivan Cheltsov, Ciro Ciliberto, Hubert Flenner, James McKernan **
cover the following topics.

Part-I Birational Automorphisms

Singular del Pezzo Fibrations and Birational Rigidity by Hamid Ahmadinezhad

Additive Actions on Projective Hypersurfaces by Ivan Arzhantsev and Andrey Popovskiy

Cremona Groups of Real Surfaces by Jérémy Blanc and Frédéric Mangolte

On Automorphisms and Endomorphisms of Projective Varieties by Michel Brion

Del Pezzo Surfaces and Local Inequalities by Ivan Cheltsov

Fano Hypersurfaces and their Birational Geometry by Tommaso de Fernex

On the Locus of Nonrigid Hypersurfaces by Thomas Eckl and Aleksandr Pukhlikov

On the Genus of Birational Maps Between Threefolds by Stéphane Lamy

On the Automorphisms of Moduli Spaces of Curves by Alex Massarenti and Massimiliano Mella

Normal Analytic Compactifications of C2 by Pinaki Mondal

Jordan Groups and Automorphism Groups of Algebraic Varieties by Vladimir L. Popov

2-Elementary Subgroups of the Space Cremona Group by Yuri Prokhorov

Birational Automorphism Groups of Projective Varieties of Picard Number Two by De-Qi Zhang

Part-II Automorphisms of Affine Varieties

Rational Curves with One Place at Infinity by Abdallah Assi

The Jacobian Conjecture, Together with Specht and Burnside-Type Problems by Alexei Belov, Leonid Bokut, Louis Rowen, and Jie-Tai Yu

Equivariant Triviality of Quasi-Monomial Triangular Ga-Actions on A4 by Adrien Dubouloz, David R. Finston, and Imad Jaradat

Automorphism Groups of Certain Rational Hypersurfaces in Complex Four-Space by Adrien Dubouloz, Lucy Moser-Jauslin, and Pierre-Marie Poloni

Laurent Cancellation for Rings of Transcendence Degree One Over a Field by Gene Freudenburg

Deformations of A1-Fibrations by Rajendra V. Gurjar, Kayo Masuda, and Masayoshi Miyanishi

Remark on Deformations of Affine Surfaces with A1-Fibrations by Takashi Kishimoto

How to Prove theWildness of Polynomial Automorphisms: An Example by Shigeru Kuroda

Flexibility Properties in Complex Analysis and Affine Algebraic Geometry by Frank Kutzschebauch

Strongly Residual Coordinates over AOEx by Drew Lewis

Configuration Spaces of the Affine Line and their Automorphism Groups by Vladimir Lin and Mikhail Zaidenberg

On the Newton Polygon of a JacobianMate by Leonid Makar-Limanov

Keller Maps of Low Degree over Finite Fields by Stefan Maubach and Roel Willems

Cancellation by Peter Russell

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