Invariants of Relative Right and Contact Equivalences

摘要: We study holomorphic function germs under equivalence relations that preserve an analytic variety. show two quasihomogeneous polynomials, not necessarily with isolated singularities, having isomorphic relative Milnor algebras are right equivalent. Under the condition module of vector fields tangent to variety is finitely generated, we also Tjurina algebra a complete invariant for classification arbitrary respect contact equivalence. This version well known result by Mather and Yau.