The Jacobian Conjecture fails for pseudo-planes

摘要

A smooth complex variety satisfies the Generalized Jacobian Conjecture if all its kale endomorphisms are proper. We study the conjecture for Q-acyclic surfaces of negative logarithmic Kodaira dimension. We show that G-equivariant counterexamples for infinite group G exist if and only if G = C* and we classify them relating them to Belyi-Shabat polynomials. Taking universal covers we get rational simply connected C*-surfaces of negative logarithmic Kodaira dimension which admit non-proper C*-equivariant kale endomorph isms.