The option PreviousGens is a list of polynomials of total degree at most $d-1$ which can be used with componentOfKernel to trim the monomial basis for that multidegree.
The object PreviousGens is a symbol.
The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/MultigradedImplicitization.m2:580:0.