The Second Main Theorem with moving hypersurfaces in subgeneral position

TL;DR

This paper extends the second main theorem in Nevanlinna theory to holomorphic curves intersecting moving hypersurfaces in subgeneral position, providing a refined inequality with a specific factor.

Contribution

It introduces a second main theorem for holomorphic curves with moving hypersurfaces in subgeneral position, improving the inequality factor based on recent research.

Findings

Established a second main theorem with a 3/2 factor.

Applied to holomorphic curves intersecting moving hypersurfaces.

Extended previous results to subgeneral position cases.

Abstract

In this paper, we prove a second main theorem for a holomorphic curve $f$ into $\mathbb P^N (\mathbb C)$ with a family of slowly moving hypersurfaces $D_1,...,D_q$ with respect to $f$ in $m$-subgeneral position, proving an inequality with factor $3 \over 2$. The motivation comes from the recent result of Heier and Levin.