Mathematical Research Letters
Volume 13 (2006)
Quartic K3 surfaces without nontrivial automorphisms
Pages: 423 – 439
For any field $k$ of characteristic at most $19$ we exhibit an explicit smooth quartic surface in $\P^3_k$ with trivial automorphism group over $\kbar$. We also show how this can be extended to higher characteristics. Over $\Q$ we construct an example on which the set of rational points is Zariski dense.