Approximately rationally or elliptically connected varieties

TL;DR

This paper explores a new approach to understanding when the Kobayashi pseudometric vanishes on projective varieties by examining chains of rational or elliptic curves near the variety in projective space.

Contribution

It introduces a novel method using chains of rational or elliptic curves in small neighborhoods to study the Kobayashi pseudometric's behavior.

Findings

Proposes a new approach to Kobayashi pseudometric analysis

Highlights the role of rational and elliptic curves in this context

Suggests potential for future research in complex geometry

Abstract

We discuss a possible approach to the study of the vanishing of the Kobayashi pseudometric of a projective variety X, using chains of rational or elliptic curves contained in an arbitrarily small neighborhood of X in projective space for the Euclidean topology.