Open surfaces of logarithmic Kodaira dimension zero in arbitrary characteristic

Abstract

In this article we study nonsingular rational open surfaces of logarithmic Kodaira dimension zero with connected boundaries at infinity defined over an algebraically closed field of arbitrary characteristic. We establish a classification theory of nonsingular alfine surfaces of logarithmic Kodaira dimension zero and give a characterization of $A_{*}^1\times A_{*}^1$ in arbitrary characteristic.