A Uniqueness Theorem for Meromorphic Maps with Moving Hypersurfaces

TL;DR

This paper proves a uniqueness theorem for certain meromorphic maps from complex Euclidean spaces into projective spaces, involving moving hypersurfaces in general position, with results depending on the hypersurfaces' degrees.

Contribution

It establishes a new uniqueness theorem for algebraically nondegenerate meromorphic maps with moving hypersurfaces, extending previous results to more general conditions.

Findings

Uniqueness theorem for meromorphic maps with moving hypersurfaces

Effective bounds on the number of hypersurfaces q

Applicable to algebraically nondegenerate maps in complex projective space

Abstract

In this paper, we establish a uniqueness theorem for algebraically nondegenerate meromorphic maps of C^m into C P^n and slowly moving hypersurfaces Q_j in C P^n, j=1,...,q in (weakly) general position, where q depends effectively on n and on the degrees d_j of the hypersurfaces Q_j.