Computations for A1, Ak, D4, E8 and other singularities show finite discriminant torsion is a codimension-two phenomenon, not generic for nodes, with threefold ordinary double points being torsion-free.
The topology of complex projective varieties after S. Lefschetz
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Torsion Trajectories from Local Discriminants to Global Obstructions
Computations for A1, Ak, D4, E8 and other singularities show finite discriminant torsion is a codimension-two phenomenon, not generic for nodes, with threefold ordinary double points being torsion-free.