2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97934Let k be a field of characteristic 0, R = k[x_1, ..., x_d] be a polynomial ring, and m its maximal homogeneous ideal. Let I be a homogeneous ideal in R. In this paper we investigate asymptotic behaviour of the quotient between the length of local cohomology group H^0_m(R/I^n) and n^d. We show that this quantity always has a limit as n goes to infinity. We also give an example for which the limit is irrational; in particular, this proves that the length of H^0_m(R/I^n) is not asymptotically a polynomial in n.To appear in Canadian Journal of Mathematics. 13 pagesCommutative AlgebraAlgebraic Geometry13D40; 14B15; 13D45text