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arXiv · 2603.22678

Picard rank jumps for families of K3 surfaces in positive characteristic

Ruofan Jiang·Ananth N. Shankar·Ziquan Yang
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Abstract

Let X/C be a non iso-trivial family of K3 surfaces over a curve C defined over characteristic p > 2 field. We show that if X avoids a necessary and structural obstruction coming from Frobenius, and satisfies a big monodromy condition, then there are infinitely may geometric fibers that have larger Picard rank than the geometric generic fiber.

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Ruofan Jiang, Ananth N. Shankar, Ziquan Yang. 2026-03-24. Picard rank jumps for families of K3 surfaces in positive characteristic. https://arxiv.org/abs/2603.22678

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