Liaison and deformation
The relation between liaison and some notions from deformation theory (as rigidity, the number of generators of the normal module, smoothability) is studied. Let \(P=kX\) be a power series ring over a field k of characteristic zero. Let I be a perfect P-ideal and let J be geometrically linked to I with respect to a regular sequence \(\alpha\). Upper and lower bounds are established for the number of generators of the normal module \(Hom_ P(J,P/J)\) in terms of the number of generators of \(Hom_ P(I,P/I)\). The number of generators of some normal modules are computed. Let I and J be perfect P-ideals in the same linkage class. It is algebraically proved that P/I is smoothable in codimension \(s\geq 3\) iff P/J has the same property.
scientific article; zbMATH DE number 3918522