Mathematics > Algebraic Geometry
[Submitted on 21 May 2018 (v1), last revised 17 Jan 2020 (this version, v4)]
Title:Rational curves on elliptic K3 surfaces
View PDFAbstract: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.
Submission history
From: Salim Tayou [view email][v1] Mon, 21 May 2018 10:31:15 UTC (8 KB)
[v2] Tue, 18 Dec 2018 18:01:01 UTC (8 KB)
[v3] Mon, 2 Dec 2019 17:05:25 UTC (11 KB)
[v4] Fri, 17 Jan 2020 16:31:37 UTC (11 KB)
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