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- W2046701017 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. We apply our results to construct an explicit algebraic point on a $K3$ surface that does not lie on any smooth rational curves." @default.
- W2046701017 created "2016-06-24" @default.
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- W2046701017 date "2007-09-05" @default.
- W2046701017 modified "2023-09-27" @default.
- W2046701017 title "K3 surfaces, rational curves, and rational points" @default.
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