A defect relation for holomorphic curves intersecting hypersurfaces

In 1933, H. Cartan proved a defect relation Sigma(j=1)(q) delta(f) (H-j) less than or equal to n + 1 for a linearly nonde generate holomorphic curve f : C --> P-n(C) and hyperplanes H-j, 1 less than or equal to j less than or equal to q, in P-n(C) in general position. This paper extends it to holomorphic curves intersecting hypersurfaces. In 1979, B. Shiffman conjectured that if f : C --> P-n(C) is an algebraically non-degenerate holomorphic map, and D-1,..., D-q are hypersurfaces in P-n(C) in general position, then Sigma(j=1)(q) delta(f)(D-j) less than or equal to n + 1. This paper proves this conjecture.