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

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.

10 pages; Example 2 replaced, and Theorem 4 improved with suggestions from an anonymous referee