Let \(\{D_{i}\}_{i=1}^{n+1}\) be n + 1 hypersurfaces in ℙn(ℂ) with total degrees \(\sum\nolimits_{i=1}^{n+1}\deg D_{i}\geqslant n+2\) , in general position and satisfying a generic geometric condition: every n hypersurfaces intersect only at smooth points, and their intersections are transversal. For every algebraically nondegenerate entire holomorphic curve f: ℂ → ℙn(ℂ), we establish a Second Main Theorem: \(\sum_{i=1}^{n+1}\delta_{f}(D_{i})<n+1,\) expressed as a defect inequality in Nevanlinna theory. This result provides the first example in the literature of a Second Main Theorem for n + 1 general hypersurfaces in ℙn(ℂ) with optimal total degrees.
