K3 surfaces, rational curves, and rational points |
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| Authors: | Arthur Baragar David McKinnon |
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| Institution: | a Department of Mathematical Sciences, University of Nevada Las Vegas, Box 454020, 4505 Maryland Parkway, Las Vegas, NV 89154-4020, USA
b Department of Pure Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada |
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| Abstract: | We prove that for any of a wide class of elliptic surfaces X defined over a number field k, if there is an algebraic point on X that lies on only finitely many rational curves, then there is an algebraic point on X that lies on no rational curves. In particular, our theorem applies to a large class of elliptic K3 surfaces, which relates to a question posed by Bogomolov in 1981. |
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| Keywords: | 14G05 11G05 11G35 |
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