  This paper deals with properties of the algebraic variety defined as the set
of zeros of a "deficient" sequence of multivariate polynomials. We consider two
types of varieties: ideal-theoretic complete intersections and absolutely
irreducible varieties. For these types, we establish improved bounds on the
dimension of the set of deficient systems of each type over an arbitrary field.
On the other hand, we establish improved upper bounds on the number of systems
of each type over a finite field.
