Nevanlinna Second Main Theorem and tautological inequality for parabolic manifolds

TL;DR

This paper extends Nevanlinna theory to parabolic manifolds, establishing a Second Main Theorem type inequality and a tautological inequality for holomorphic maps and logarithmic pairs, respectively.

Contribution

It introduces a novel Second Main Theorem inequality for holomorphic maps from parabolic manifolds and a tautological inequality for smooth logarithmic pairs.

Findings

Established a Second Main Theorem inequality for maps from parabolic manifolds.

Derived a tautological inequality for smooth logarithmic pairs.

Extended Nevanlinna theory to a broader class of manifolds.

Abstract

We obtain a Second Main Theorem type inequality for holomorphic maps $f : M \to X$, where $M$ is a parabolic manifold and $X$ is smooth projective with dim $M$ $\le$ dim $X$. We also derive a parabolic Tautological inequality for smooth logarithmic pairs.