Multiplier Ideals of Sufficiently General Polynomials

It is well known that the multiplier ideal J (r · a) of an ideal a determines in a straightforward way the multiplier ideal J (r ·f) of a sufficiently general element f of a. We give an explicit condition on a polynomial f ∈ C[x1, . . . , xn] which guarantees that it is a sufficiently general element of the most natural associated monomial ideal, the ideal generated by its terms. This allows us to directly calculate the multiplier ideal J (r · f) (for all r) of “most” polynomials f .