ON THE CONTACT COHOMOLOGY OF ISOLATED HYPERSURFACE SINGULARITIES

The author defines, using jest, cohomology H(p)(LAMBDA(f,k-.)) for hyp ersurfaces, which are invariant under contact transformations. For iso lated hypersurface singularities, it is proved that H-0(LAMBDA(f,k-.). ) = O(U,0)/f(k+1)O(U,0), H(p)(LAMBDA(f,k-.).) = 0, 1 less-than-or-equa l-to p less-than-or-equal-to N - 3 or p = N, dim H(N-2)(LAMBDA(f,k-.). ) - dim H(N-1)(LAMBDA(f,k-.).) = k/N dim O(U,0)/(f, partial derivative f/partial derivative x1,...,partial derivative f/partial derivative x (N)) O(U,0). The algorithm of computation of H(N-2) and H(N-1) is give n, and it is proved that H(N-1) = 0 when f is quasi-homogeneous.