The present volume grew out of an international conference on affine algebraic geometry held in Osaka, Japan during 3-6 March 2011 and is dedicated to Professor Masayoshi Miyanishi on the occasion of his 70th birthday. It contains 16 refereed articles in the areas of affine algebraic geometry, commutative algebra and related fields, which have been the working fields of Professor Miyanishi for almost 50 years. Readers will be able to find recent trends in these areas too. The topics contain both algebraic and analytic, as well as both affine and projective, problems. All the results treated in this volume are new and original which subsequently will provide fresh research problems to explore. This volume is suitable for graduate students and researchers in these areas.
Acyclic Curves and Group Actions on Affine Toric Surfaces (Arzhantsev and M Zaidenberg); Cyclic Multiple Planes, Branched Covers of Sn and a Result of D L Goldsmith (R V Gurjar); A1*-Fibrations on Affine Threefolds (R V Gurjar, M Koras, K Masuda, M Miyanishi and P Russell); Hirzeburch Surfaces and Compactifications of C2 (A Ishida and M Furushima); A Galois Counterexample to Hilbert's Fourteenth Problem in Dimension Three with Rational Coefficients (E Kobayashi and S Kuroda); Open Algebraic Surfaces of Logarithmic Kodaira Dimension One (H Kojima); Abhyankar - Sathaye Embedding Conjecture for a Geometric Case (T Ohta); Some Subgroups of the Cremona Groups (V Popov); Representations of Ga of Codimension Two (R Tanimoto); On Unicuspidal Plane Curves of Genus Two (K Tono); Sextic Variety as Galois Closure Variety of Smooth Cubic (H Yoshihara); Invariant Hypersurfaces of Endomorphisms of the Projective 3-Space (De-Qi Zhang); Some Properties of C* in C2 (M Koras and P Russell); Examples of Non-Uniruled Surfaces with Pre-Tango Structures involving Non-Closed Global Differential 1-Forms (Y Takeda); Miyanishi's Characterization of Singularities Appearing on A1-Fibrations Does Not Hold in Higher Dimensions (T Kishimoto); The Gonality of Singular Plane Curves II (F Sakai).