Mathematical Research Letters

Volume 13 (2006)

Number 3

Quartic K3 surfaces without nontrivial automorphisms

Pages: 423 – 439



Ronald van Luijk (University of California at Berkeley)


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.

Published 1 January 2006