Abstract
Let I be a homogeneous ideal in a positively graded affine k-algebra (where k is an infinite field). We characterize the scheme-theoretic generations J of I which are reductions of I; we deduce that l(I) ≤ σ(I) where l(I) is the analytic spread of I and σ(I) denotes the minimal number of the scheme-theoretic generations of I. As application, in the polynomial ring k[x 0,…,x d − 1], we prove the uniqueness of the degrees of every scheme-th. generation of minimal length for a quasi complete intersection I when codim(I) < d − 1.
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