Variation of Neron-Severi ranks of reductions of K3 surfaces

Edgar Costa; Yuri Tschinkel

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arXiv · 1405.2265

Variation of Neron-Severi ranks of reductions of K3 surfaces

Edgar Costa·Yuri Tschinkel

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Abstract

We study the behavior of geometric Picard ranks of K3 surfaces over the rationals 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.

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Edgar Costa, Yuri Tschinkel. 2014-05-09. Variation of Neron-Severi ranks of reductions of K3 surfaces. https://arxiv.org/abs/1405.2265

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