Rational curves on elliptic K3 surfaces

Salim Tayou

Rational curves on elliptic K3 surfaces

Algebraic Geometry 2020-01-20 v4

Authors: Salim Tayou

Abstract

We prove that any non-isotrivial elliptic K3 surface over an algebraically closed field $k$ of arbitrary characteristic contains infinitely many rational curves. In the case when $\mathrm{char}(k)\neq 2,3$ , we prove this result for any elliptic K3 surface. When the characteristic of $k$ is zero, this result is due to the work of Bogomolov-Tschinkel and Hassett.

Keywords

rational points on curves algebraic surfaces elliptic curves

Cite

@article{arxiv.1805.07975,
  title  = {Rational curves on elliptic K3 surfaces},
  author = {Salim Tayou},
  journal= {arXiv preprint arXiv:1805.07975},
  year   = {2020}
}

Comments

Lemma 2.4 (2) fixed. To appear in Mathematical Research Letters

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