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Results tagged with k3-surfaces
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user 17907
Questions about K3 surfaces, which are smooth complex surfaces $X$ with trivial canonical bundle and vanishing $H^1(O_X)$. They are examples of Calabi-Yau varieties of dimension $2$.
5
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2
answers
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Singular models of K3 surfaces
Let us work over a ground field of characteristic zero. As is well-known, a K3 surface is a smooth projective geometrically integral surface $X$ whose canonical class $\omega_X$ is trivial and for whi …
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5
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Singular models of K3 surfaces
For what it's worth, I wrote up a proof (pretty detailed) following the hints in Francesco Polizzi's answer. It's in an unpublished preprint found here (p. 38 onwards). I am not a geometer, so the exp …
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2
votes
Elliptic fibration of K3 surface
In characteristic $0$, I think the answer is yes, since $U(k)$ contains elements with square zero. See Theorem 11.1 in Brendan Hassett, Potential density of rational points on algebraic varieties (pdf …
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