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- W2951504199 abstract "We study non-isotrivial families of $K3$ surfaces in positive characteristic $p$ whose geometric generic fibers satisfy $rhogeq21-2h$ and $hgeq3$, where $rho$ is the Picard number and $h$ is the height of the formal Brauer group. We show that, under a mild assumption on the characteristic of the base field, they have potential supersingular reduction. Our methods rely on Maulik's results on moduli spaces of $K3$ surfaces and the construction of sections of powers of Hodge bundles due to van der Geer and Katsura. For large $p$ and each $2leq{h}leq10$, using deformation theory and Taelman's methods, we construct non-isotrivial families of $K3$ surfaces satisfying $rho=22-2h$." @default.
- W2951504199 created "2019-06-27" @default.
- W2951504199 creator A5007563811 @default.
- W2951504199 date "2016-11-15" @default.
- W2951504199 modified "2023-10-16" @default.
- W2951504199 title "Existence of supersingular reduction for families of K3 surfaces with large Picard number in positive characteristic" @default.
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- W2951504199 doi "https://doi.org/10.48550/arxiv.1611.04721" @default.
- W2951504199 hasPublicationYear "2016" @default.
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