Effective Nullstellensatz and geometric degree for zero-dimensional ideals

On some generalizations of Jacobi's residue formula

“…As a consequence, it will be then natural to present in section 4 some applications of our two theorems to effectivity questions related to the algebraic Nullstellensatz in the projective case or the sparse Nullstellensatz in the toric case, under some properness assumptions on the data in C n or in T n . Such results will extend or sharpen some previous results in [6,7,15,30]. We will also suggest possible applications to some results of Cayley-Bacharach type (see [14]), in the context of improper intersections on P n or on a smooth toric variety X .…”

Residue Currents

“…. , P n ) is a proper polynomial map from C n to C n ), we refer to [36,91], Sec. 4; with respect to the second example (entries defining a complete intersection), we refer to [9,28,34].…”