Irrational open surfaces of non-negative logarithmic Kodaira dimension

Abstract

We study irrational open algebraic surfaces of non-negative logarithmic Kodaira dimension in any characteristic. We give a structure theorem for the irrational open surfaces of logarithmic Kodaira dimension zero. Then, by using this result and the results in [7], we prove that, for an irrational ruled open surface, its logarithmic Kodaira dimension is non-negative if and only if its logarithmic bigenus is positive.