Variation of Néron–Severi Ranks of Reductions of K3 Surfaces

Edgar Costa, Yuri Tschinkel
2014 Experimental Mathematics  
We study the behavior of geometric Picard ranks of K3 surfaces over Q under reduction modulo primes. We compute these ranks for reductions of smooth quartic surfaces modulo all primes p < 2 16 in several representative examples and investigate the resulting statistics.
doi:10.1080/10586458.2014.947054 fatcat:3kkey5evtfflddkmgi33pfafm4