Abstract
In this paper we obtain an effective Nullstellensatz using quantitative considerations of the classical duality theory in complete intersections. Letk be an infinite perfect field and let f1,...,f n−r∈k[X1,...,Xn] be a regular sequence with d:=maxj deg fj. Denote byA the polynomial ringk [X1,..., Xr] and byB the factor ring k[X1,...,Xn]/(f1,...,fnr); assume that the canonical morphism A→B is injective and integral and that the Jacobian determinantΔ with respect to the variables Xr+1,...,Xn is not a zero divisor inB. Let finally σ∈B*:=HomA(B, A) be the generator of B* associated to the regular sequence.
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