Kummer surfaces and the computation of the Picard group
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چکیده
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 P. Using the theory of abelian varieties, in this case the Picard group may be computed directly. Our experiments show that the upper bounds provided by R. van Luijk’s method are sharp when sufficiently large primes are used. In fact, there are many primes which yield the exact value. However, for many but not all Kummer surfaces V of Picard rank 18, we have rk Pic(VFp) ≥ 20 for a set of primes of density ≥ 12 .
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تاریخ انتشار 2010