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.
Koll\'ar, Families of varieties of general type, Cambridge Tracts in Mathematics, vol
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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.