AUTOMORPHISMS IN BIRATIONAL AND AFFINE GEOMETRY

- Presents original research and valuable overview on topics such as Cremona groups, birational rigidity, dynamics of automorphisms, and algebraic group actions.
- Features articles by leading specialists in the field.
- Compares and contrasts different views on the problem of describing the automorphism groups of affine and projective varieties.
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.

Table of contents (27 chapters)
1.Singular del Pezzo Fibrations and Birational Rigidity
2.Additive Actions on Projective Hypersurfaces
3.Cremona Groups of Real Surfaces
4.On Automorphisms and Endomorphisms of Projective Varieties
5.Del Pezzo Surfaces and Local Inequalities
6.Fano Hypersurfaces and their Birational Geometry
7.On the Locus of Nonrigid Hypersurfaces
8.On the Genus of Birational Maps Between Threefolds
9.On the Automorphisms of Moduli Spaces of Curves
10.Normal Analytic Compactifications of
11.Jordan Groups and Automorphism Groups of Algebraic Varieties
12.2-Elementary Subgroups of the Space Cremona Group
13.Birational Automorphism Groups of Projective Varieties of Picard Number Two
14.Rational Curves with One Place at Infinity
15.The Jacobian Conjecture, Together with Specht and Burnside-Type Problems
16.Equivariant Triviality of Quasi-Monomial Triangular
17.Automorphism Groups of Certain Rational Hypersurfaces in Complex Four-Space
18.Laurent Cancellation for Rings of Transcendence Degree One Over a Field
19.Deformations of
20.Remark on Deformations of Affine Surfaces with
21.How to Prove the Wildness of Polynomial Automorphisms: An Example
22.Flexibility Properties in Complex Analysis and Affine Algebraic Geometry
23.Strongly Residual Coordinates over
24.Configuration Spaces of the Affine Line and their Automorphism Groups
25.On the Newton Polygon of a Jacobian Mate
26.Keller Maps of Low Degree over Finite Fields
27.Cancellation