Hilbert-Samuel coefficients and postulation numbers of graded components of certain local cohomology modules

M Brodmann, F Rohrer
Let R = n≥0 Rn be a Noetherian homogeneous ring with onedimensional local base ring (R 0 , m 0 ). Let q 0 ⊆ R 0 be an m 0 -primary ideal, let M be a finitely generated graded R-module and let i ∈ N 0 . Let H i R + (M ) denote the i-th local cohomology module of M with respect to the irrelevant ideal R + := n>0 Rn of R. We show that the first Hilbert-Samuel coefficient e 1 q 0 , H i R + (M )n of the n-th graded component of H i R + (M ) with respect to q 0 is antipolynomial of degree < i in n.
more » ... degree < i in n. In addition, we prove that the postulation numbers of the components H i R + (M )n with respect to q 0 have a common upper bound.
doi:10.5167/uzh-21680 fatcat:gjm3k5zgsvcjrftcu7jarjlnji