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Quartic K3 surfaces without nontrivial automorphisms

Ronald van Luijk
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Abstract

For any field k of characteristic at most 5 we exhibit an explicit smooth quartic surface in projective threespace over k with trivial automorphism group over the algebraic closure of k. We also show how this can be extended to higher characteristics. Over the rationals we construct an example on which the set of rational points is Zariski dense.

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Ronald van Luijk. 2005-11-22. Quartic K3 surfaces without nontrivial automorphisms. https://arxiv.org/abs/math/0511542

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