One-dimensional Local Families of Complex K3 Surfaces
Abstract
For any complex K3 surface X, we construct a one-dimensional deformation in which all integers with 0 ≤ ≤ 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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