Density of Rational Curves on K3 Surfaces

TL;DR

This paper demonstrates that on a very general K3 surface, rational curves are densely distributed, and elliptic curves are densely distributed in the 1st jet space, revealing rich geometric structures.

Contribution

It proves the density of rational and elliptic curves on very general K3 surfaces, advancing understanding of their geometric properties.

Findings

Rational curves are dense on very general K3 surfaces.

Elliptic curves are dense in the 1st jet space of such surfaces.

Both density results hold in the strong topology.

Abstract

We proved that the union of rational curves is dense on a very general K3 surface and the union of elliptic curves is dense in the 1st jet space of a very general K3 surface, both in the strong topology.