Properties of the fiber cone of ideals in local rings

F or an ideal I of a Noetherian local ring (R, m) we consider properties of I and its powers as reflected in the fiber cone F(I) of L In particular, we examine behavior of the fiber cone under homomorphic image R --> R/J= R' as related to analytic spread and generators for the kernel of the induced map on fiber cones psi(J):F(R)(I) --> F(R')(IR'). We consider the structure of fiber cones F(I) for which ker psi(J) not equal 0 for each nonzero ideal J of R. If dim F(I) = d > 0, mu(I) = d+ 1 and there exists a minimal reduction J of I generated by a regular sequence, we prove that if grade(G(+)(I)) greater than or equal to d - 1, then F(I) is Cohen-Macaulay and thus a hypersurface.