On the depth of the tangent cone and the growth of the Hilbert function

Elías García, Joan2009-04-162009-04-1619991088-6850https://hdl.handle.net/2445/7766For a d-dimensional Cohen-Macaulay local ring (R,m) we study the depth of the associated graded ring of R with respect to an m-primary ideal I in terms of the Vallabrega-Valla conditions and the length of It+1/JIt, where J is a J minimal reduction of I and t≥ 1. As a corollary we generalize Sally's conjecture on the depth of the associated graded ring with respect to a maximal ideal to m-primary ideals. We also study the growth of the Hilbert function.17 p.application/pdfeng(c) American Mathematical Society, 1999Anells localsIdeals (Àlgebra)HomologiaFuncions característiquesGeometria algebraicaAssociated graded rings of idealsHomological methodsHilbert-Samuel and Hilbert-Kunz functionsPoincaré seriesLocal rings and semilocal ringsOn the depth of the tangent cone and the growth of the Hilbert functioninfo:eu-repo/semantics/article153816info:eu-repo/semantics/openAccess