TL;DR
This paper proves the existence of rational curves in all linear systems on general K3 surfaces and shows that all such curves in the hyperplane class are nodal for small genus, advancing understanding of their geometric properties.
Contribution
It establishes the existence of rational curves in every linear system on general K3 surfaces and characterizes their nodal nature in the hyperplane class for small genus.
Findings
Rational curves exist in every linear system on a general K3 surface.
All rational curves in the hyperplane class are nodal on a general K3 surface of small genus.
The results deepen the understanding of the geometry of K3 surfaces.
Abstract
We proved the existence of rational curves in every linear system on a general K3 surface and that all rational curves in the hyperplane class are nodal on a general K3 surface of small genus.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Geometric Analysis and Curvature Flows