ABSTRACT
We continue with the discussion of the resultant ideal introduced in the last section. As there let A be an integrally closed noetherian domain, F 0, …, Fn a regular sequence of homogeneous polynomials in the polynomial ring A[T] = A[T 0 , …, Tn ] and C ≔ A[T]/(F 0, …, Fn ). We will show now that the resultant ideal R = R(F 0, …, Fn ) describes exactly the divisorial part of the A-algebra of global sections in OProj C , which is annihilated by the elimination ideal T0 and therefore an algebra over A ¯ = A / T 0 = C ¯ 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064265/27e88de8-b4c2-47de-a1e8-3cf9bc1ec436/content/inequ14_109_1.tif"/> in a natural way, cf. [44].
