a1 Mathematisches Institut, Universität Bayreuth, Universitätsstr. 30, D-95440 Bayreuth, Germany (email: Stephan.Elsenhans@uni-bayreuth.de)
a2 Department Mathematik, Universität Siegen, Walter-Flex-Str. 3, D-57068 Siegen, Germany (email: email@example.com)
We test R. van Luijk’s method for computing the Picard group of a K3 surface. The examples considered are the resolutions of Kummer quartics in 3. Using the theory of abelian varieties, the Picard group may be computed directly in this case. Our experiments show that the upper bounds provided by van Luijk’s method are sharp when sufficiently many primes are used. In fact, there are a lot of primes that yield a value close to the exact one. However, for many but not all Kummer surfaces V of Picard rank 18, we have for a set of primes of density at least 1/2.
(Received September 03 2010)
(Revised September 22 2011)
(Online publication April 2012)
2010 Mathematics Subject Classification