One-dimensional Local Families of Complex K3 Surfaces

Published 26 Sep 2022 in math.AG | (2209.13003v1)

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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