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E-grāmata: Automorphisms in Birational and Affine Geometry: Levico Terme, Italy, October 2012

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The main focus of this 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.

PART I Birational Automorphisms
Singular del Pezzo Fibrations and Birational Rigidity
3(14)
Hamid Ahmadinezhad
Additive Actions on Projective Hypersurfaces
17(18)
Ivan Arzhantsev
Andrey Popovskiy
Cremona Groups of Real Surfaces
35(24)
Jeremy Blanc
Frederic Mangolte
On Automorphisms and Endomorphisms of Projective Varieties
59(24)
Michel Brion
Del Pezzo Surfaces and Local Inequalities
83(20)
Ivan Cheltsov
Fano Hypersurfaces and their Birational Geometry
103(18)
Tommaso de Fernex
On the Locus of Nonrigid Hypersurfaces
121(20)
Thomas Eckl
Aleksandr Pukhlikov
On the Genus of Birational Maps Between Threefolds
141(8)
Stephane Lamy
On the Automorphisms of Moduli Spaces of Curves
149(1)
Alex Massarenti
Massimiliano Mella
Normal Analytic Compactifications of C2
149(36)
Pinaki Mondal
Jordan Groups and Automorphism Groups of Algebraic Varieties
185(30)
Vladimir L. Popov
2-Elementary Subgroups of the Space Cremona Group
215(16)
Yuri Prokhorov
Birational Automorphism Groups of Projective Varieties of Picard Number Two
231(10)
De-Qi Zhang
PART II Automorphisms of Affine Varieties
Rational Curves with One Place at Infinity
241(8)
Abdallah Assi
The Jacobian Conjecture, Together with Specht and Burnside-Type Problems
249(38)
Alexei Belov
Leonid Bokut
Louis Rowen
Jie-Tai Yu
Equivariant Triviality of Quasi-Monomial Triangular Ga-Actions on A4
287(14)
Adrien Dubouloz
David R. Finston
Imad Jaradat
Automorphism Groups of Certain Rational Hypersurfaces in Complex Four-Space
301(12)
Adrien Dubouloz
Lucy Moser-Jauslin
Pierre-Marie Poloni
Laurent Cancellation for Rings of Transcendence Degree One Over a Field
313(14)
Gene Freudenburg
Deformations of A1-Fibrations
327(36)
Rajendra V. Gurjar
Kayo Masuda
Masayoshi Miyanishi
Remark on Deformations of Affine Surfaces with A1-Fibrations
363(18)
Takashi Kishimoto
How to Prove the Wildness of Polynomial Automorphisms: An Example
381(6)
Shigeru Kuroda
Flexibility Properties in Complex Analysis and Affine Algebraic Geometry
387(20)
Frank Kutzschebauch
Strongly Residual Coordinates over A[ x]
407(24)
Drew Lewis
Configuration Spaces of the Affine Line and their Automorphism Groups
431(38)
Vladimir Lin
Mikhail Zaidenberg
On the Newton Polygon of a Jacobian Mate
469(8)
Leonid Makar-Limanov
Keller Maps of Low Degree over Finite Fields
477(18)
Stefan Maubach
Roel Willems
Cancellation
495
Peter Russell