Deficiencies of meromorphic mappings for hypersurfaces

抄録

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.