A defect relation for holomorphic curves intersecting hypersurfaces

In 1933, H. Cartan proved a defect relation Σ^q_j=1 δ_f (H_j) ≤ n + 1 for a linearly nondegenerate holomorphic curve f : [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] and hyperplanes H_j, 1 ≤ j ≤ q, in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /] in general position. This paper extends it to holomorphic curves intersecting hypersurfaces. In 1979, B. Shiffman conjectured that if f : [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="03i" /] is an algebraically non-degenerate holomorphic map, and D₁, . . . ,D_q are hypersurfaces in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="04i" /] in general position, then Σ^q_j=1 δ_f (D_j) ≤ n + 1. This paper proves this conjecture.