Nevanlinna theory for holomorphic curves from annuli into semi Abelian varieties

TL;DR

This paper extends Nevanlinna theory to holomorphic curves from annuli into semi-Abelian varieties, providing a key lemma and a second main theorem for such curves intersecting a single divisor.

Contribution

It introduces a logarithmic derivative lemma and a second main theorem specifically for holomorphic curves from annuli into semi-Abelian varieties, advancing value distribution theory.

Findings

Proved a logarithmic derivative lemma for these curves.

Established a second main theorem for curves intersecting one divisor.

Enhanced understanding of value distribution in complex geometry.

Abstract

In this paper, we prove a lemma on logarithmic derivative for holomorphic curves from annuli into K\"{a}hler compact manifold and. As its application, a second main theorem for holomophic curves from annuli into semi abelian varieties intersecting with only one divisor is given.