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Let $\{D_i\}_{i=1}^{n+1}$ be $n+1$ hypersurfaces in$\mathbb{P}^n(\mathbb{C})$ with total degrees $\sum_{i=1}^{n+1} \degD_i\geqslant n+2$, in general position and satisfying a generic geometriccondition: every $n$ hypersurfaces intersect only at smooth points and theintersection is transversal. Then, for every algebraically nondegenerate entireholomorphic curve $f\colon\mathbb{C}\rightarrow\mathbb{P}^n(\mathbb{C})$, weshow a Second Main Theorem: $$ \sum_{i=1}^{n+1} \delta_f(D_i) < n+1 $$ in termsof defect inequality in Nevanlinna theory. This is the first result in theliterature on Second Main Theorem for $n+1$ general hypersurfaces in$\mathbb{P}^n(\mathbb{C})$ with optimal total degrees.

Entire holomorphic curves into $\mathbb{P}^n(\mathbb{C})$ intersecting $n+1$ general hypersurfaces