Deficiencies of meromorphic mappings for hypersurfaces

Abstract

In this paper we first prove that, for every hypersurface $D$ of degree $d$ in a complex projective space, there exists a holomorphic curve $f$ from the complex plane into the projective space whose deficiency for $D$ is positive and less than one. Using this result, we construct meromorphic mappings from the complex $m$-space into the complex projective space with the same properties. We also investigate the effect of resolution of singularities to defects of meromorphic mappings.