Quartic K3 surfaces without nontrivial automorphisms

Details Quartic K3 surfaces without nontrivial automorphisms Quartic K3 surfaces without nontrivial automorphisms

2005-11-22

arxiv.org/abs/math/0511542v1

Mathematics

Algebraic Geometry

13 pages

Scientific paper

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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