Nonisolated Saito singularities

A. G. Aleksandrov

Sbornik. Mathematics, Tome 65 (1990) no. 2, pp. 561-574

Résumé

It is proved that Saito divisors are characterized by the property that their singularities form a Cohen–Macaulay space. It is shown that this property is enjoyed by the discriminant of a miniversal deformation of a complete intersection with an isolated singularity. This gives a new proof of the fact that such a discriminant is a free divisor. As one example, generators are explicitly computed for the module of vector fields tangent to the discriminant of a miniversal deformation of the simple one-dimensional Giusti singularity $S_5$ – an intersection of two quadrics in three-space. It is also explained how the theory of local duality for isolated singularities can be carried over to the case of nonisolated Saito singularities. Bibliography: 37 titles.