Constructing rational curves on K3 surfaces
Algebraic Geometry
2019-12-19 v1
Abstract
We develop a mixed-characteristic version of the Mori-Mukai 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.
Cite
@article{arxiv.0907.3527,
title = {Constructing rational curves on K3 surfaces},
author = {Fedor Bogomolov and Brendan Hassett and Yuri Tschinkel},
journal= {arXiv preprint arXiv:0907.3527},
year = {2019}
}
Comments
19 pages