Mathematical Research Letters

Volume 13, Issue 3, May 2006 pp. 423-439.

Quartic K3 surfaces without nontrivial automorphisms

Authors: Ronald van Luijk
Author institution: University of California, Berkeley

Summary: 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.

Contents Full-Text PDF