Numerically trivial divisors on families extend after a weak semi-stable reduction when the base is a curve, but fail to extend in base dimensions at least two.
Friedman, Algebraic surfaces and holomorphic vector bundles, Universitext, Springer-Verlag, New York (1998)
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The extension of numerically trivial divisors on a family
Numerically trivial divisors on families extend after a weak semi-stable reduction when the base is a curve, but fail to extend in base dimensions at least two.