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arXiv · 2306.14743

Holomorphic mappings of maximal rank into projective spaces

Dinh Tuan Huynh
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Abstract

Let $1\leq p\leq n$ be two positive integers. For a linearly nondegenerate holomorphic mapping $f\colon\mathbb{C}^p\rightarrow\mathbb{P}^n(\mathbb{C})$ 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.

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Dinh Tuan Huynh. 2023-06-26. Holomorphic mappings of maximal rank into projective spaces. https://arxiv.org/abs/2306.14743

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