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arXiv · 2209.13003

One-dimensional Local Families of Complex K3 Surfaces

Riccardo Carini·Francesco Viganò
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Abstract

For any complex K3 surface $X$, we construct a one-dimensional deformation in which all integers $\rho$ with $0 \leq \rho \leq 20$ occur as Picard numbers of some fibres. In contrast, we prove that the generic one-dimensional local family of K3 surfaces admits only $0$ and $1$ as Picard numbers of the fibres.

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Riccardo Carini, Francesco Viganò. 2022-09-26. One-dimensional Local Families of Complex K3 Surfaces. https://doi.org/10.1112/blms.12932

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