Some results on open algebraic surfaces of logarithmic Kodaira dimension zero

摘要

Let S be a smooth open algebraic surface of logarithmic Kodaira dimension zero and (V, D) a pair of a smooth projective surface V and a simple normal crossing divisor D on V such that V - D congruent to S. We prove that rho(V) - #D >= -2, where #D is the number of all irreducible components of Supp D, and determine the surface S with rho(V) - #D = -2 and those with rho(V) - #D = -1 and (p) over bar (g) (S) = 0. Furthermore, by using these results, we determine the affine plane curves whose complements have logarithmic Kodaira dimension zero. (C) 2019 Elsevier Inc. All rights reserved.