Let F1,…, Fn be homogeneous polynomials of positive degrees in the polynomial algebra A[T] = A[T0,…, Tn] graded by arbitrary positive integral weights for the indeterminates such that D: = A[T]/(F1,…, Fn) is a complete intersection of relative dimension 1 over the commutative noetherian ring A. Then Proj D is an affine scheme over A and its algebra B: = Γ(Proj D) of global sections is finite and stably free. A formula for the discriminant dB|A = Discr(F1,…, Fn) of B over A is given generalizing the well-known formula for the discriminant of an A-algebra of type A[X]/(G), where G is a monic polynomial in one variable. The formula is a special case of a result on discriminants for A-bilinear forms on B derived from linear forms B → A. The general formula uses the description of the linear forms on B with the help of a duality theory for D and the theory of resultants.
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