Affine Algebraic Geometry

Open problems in affine algebraic geometry (collected by G. Freudenburg and P. Russell) Purely inseparable $k$-forms of affine algebraic curves by T. Asanuma Generic fibrations by $A^1$ and $A^*$ over discrete valuation rings by T. Asanuma, S. M. Bhatwadekar, and N. Onoda Hesse and the Jacobian Conjecture by M. de Bondt and A. van den Essen Bad field generators by P. Cassou-Nogues Coordinates in ideals of polynomial algebras by V. Drensky On the uniqueness of $/mathbb{C}^*$-actions on affine surfaces by H. Flenner and M. Zaidenberg On two recent views of the Jacobian Conjecture by T. Kambayashi and M. Miyanishi Singularities on normal affine 3-folds containing $/mathbb{A}^1$-cylinderlike open subsets by T. Kishimoto Free $/mathbb{C}^+$-actions on affine threefolds by H. Kraft Again $x+x^2y+z^2+t^3=0$ by L. Makar-Limanov Equivariant cancellation for algebraic varieties by K. Masuda and M. Miyanishi Constructing polynomial mappings using non-commutative algebras by R. Peretz On the generic curve of genus 3 by T. Shaska and J. L. Thompson Orders of points on elliptic curves by I. E. Shparlinski Test polynomials, retracts, and the Jacobian conjecture by V. Shpilrain and J.-T. Yu The Jacobian Conjecture: ideal membership questions and recent advances by D. Wright.