Constructing rational curves on K3 surfaces

By F. Bogomolov, Brendan Hassett, Yuri Tschinkel. 2009

62 citations recorded by the source corpus.

We develop a mixed-characteristic version of the MoriMukai technique for producing rational curves on K3 surfaces. We reduce modulo p, produce rational curves on the resulting K3 surface over a finite field, and lift to characteristic zero. As an application, we prove that all complex K3 surfaces with Picard group generated by a class of degree two have an infinite number of rational curves.

Subfields: Algebra and Number Theory, Geometry and Topology, Information Systems

View Paper: https://www.semanticscholar.org/paper/7205845550e3626528ab30a39c22015d572917d8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

In Information Systems

Citations in the corpus

Rational curves on K3 surfaces (2010, background): “nitely many rational curves on very general complex projective K3 surfaces. Since then, inﬁnitely many rational curves have been established on polarized K3 surfaces of degree 2 and Picard rank ρ = 1 [BHT], elliptic K3 surfaces [BT], and K3 surfaces with inﬁnite automorphism groups. In particular, t”
Lectures on K3 Surfaces (2016, methodology): “For this chapter we highly recommend the paper [68] by Bogomolov, Hassett, and Tschinkel and Hassett’s survey [237].”
On the Picard number of K3 surfaces over number fields (2011, methodology): “This striking fact has been recently used in a surprising way by Bogomolov-Hassett-Tschinkel in [2] and Li-Liedtke in [13] to prove that any complex K3 surface with odd Picard rank contains infinitely many rational curves.”