Holomorphic mappings of maximal rank into projective spaces

Let $1\le p\le n$ be two positive integers. For a linearly nondegenerate holomorphic mapping $f\text{\hspace{0.17em}⁣}:{\mathbb{C}}^p\to {\mathbb{P}}^n(\mathbb{C})$ of maximal rank intersecting a family of hyperplanes in general position, we obtain a Cartan’s type Second Main Theorem in which the counting functions are truncated to level $n+1-p$. Our result strengthens the classical results of Stoll and Vitter, and interpolates the important works of Cartan and Carlson-Griffiths.