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Let $1\leq p\leq n$ be two positive integers. For a linearly nondegenerateholomorphic mapping $f\colon\mathbb{C}^p\rightarrow\mathbb{P}^n(\mathbb{C})$ ofmaximal rank intersecting a family of hyperplanes in general position, weobtain a Cartan's type Second Main Theorem in which the counting functions aretruncated to level $n+1-p$. Our result strengthens the classical results ofStoll and Vitter, and interpolates the important works of Cartan andCarlson-Griffiths.

Holomorphic mappings of maximal rank into projective spaces