Deformations of Functions and F-Manifolds

We study deformations of functions on isolated singularities.A unified proof of the equality of Milnor and Tjurina numbersfor functions on isolated complete intersections singularitiesand space curves is given. As a consequence, the base spaceof their miniversal deformations is endowed with the structureof an F-manifold, and we can prove a conjecture of V. Goryunov,stating that the critical values of the miniversal unfoldingof a function on a space curve are generically local coordinateson the base space of the deformation. 2000 Mathematics SubjectClassification 32S05.