A Non-Archimedean Second Main Theorem for Hypersurfaces in Subgeneral Position

TL;DR

This paper extends the second main theorem to non-Archimedean analytic maps intersecting hypersurfaces in subgeneral position, improving existing inequalities especially for non-linear, transverse hypersurfaces.

Contribution

It introduces a non-truncated second main theorem for non-Archimedean maps approximating hypersurfaces in subgeneral position, enhancing previous results by Quang.

Findings

Improves inequality bounds for non-Archimedean maps and hypersurfaces

Applicable to non-linear, transverse hypersurfaces in subgeneral position

Provides sharper results than previous theorems in specific cases

Abstract

We apply an idea of Levin to obtain a non-truncated second main theorem for non-Archimedean analytic maps approximating algebraic hypersurfaces in subgeneral position. In some cases, for example when all the hypersurfaces are non-linear and all the intersections are transverse, this improves an inequality of Quang, whose inequality is sharp for the case of hyperplanes in subgeneral position.