Rational connectedness and order of non-degenerate meromorphic maps from\ ${\bf C}^n$

TL;DR

This paper proves that compact Kähler manifolds with certain non-degenerate meromorphic maps of order less than 2 are rationally connected, linking complex analysis and algebraic geometry.

Contribution

It establishes a new criterion connecting the order of meromorphic maps from ^n to the rational connectedness of the manifold.

Findings

Manifolds with ^n  meromorphic maps of order < 2 are rationally connected.

The order of the map  ^n influences the geometric property of the manifold.

Provides a bridge between complex analysis and algebraic geometry in the context of Ka4hler manifolds.

Abstract

We show that an $n$-dimensional compact K\"ahler manifold $X$ admitting a non-degenerate meromorphic map $f:{\bf C}^n\to X$ of order $\rho_f<2$ is rationally connected.