Invariants of $R_v$-Equivalence

We recall Mather's Lemma providing effective necessary and sufficient conditions for a connected submanifold to be contained in an orbit. In Theorem 5.2 we show that two quasihomogeneous polynomials $f$ and $g$ having isomorphic relative Milnor algebras $M_v(f)$ and $M_v(g)$ are $R_v$-equivalent. In Theorem 5.4 we prove that two complex-analytic hypersurfaces, one is quasihomogeneous and other is arbitrary, are determined by isomorphism of Jacobean ideals. The Example of Gaffney and Hauser, in 1985, suggests us that we can not extend our results for arbitrary analytic germs.