∂¯ cohomology of the complement of a semi-positive anticanonical divisor of a compact surface.

Let X be a non-singular compact complex surface such that the anticanonical line bundle admits a smooth Hermitian metric with semi-positive curvature. For a non-singular hypersurface Y which defines an anticanonical divisor, we investigate the ∂ ¯ cohomology group H 1 (M , O M) of the complement M = X \ Y . [ABSTRACT FROM AUTHOR]