Rendiconti del Seminario Matematico della Università di Padova

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Published online first: 2018-11-20
DOI: 10.4171/RSMUP/11

On the monotonicity of Hilbert functions

Tony J. Puthenpurakal[1]

(1) Indian Institute of Technology Bombay, Mumbai, India

In this paper we show that a large class of one-dimensional Cohen–Macaulay local rings $(\mathcal A,\mathfrak m)$ has the property that if $M$ is a maximal Cohen–Macaulay $A$-module then the Hilbert function of $M$ (with respect to $\mathfrak m$) is non-decreasing. Examples include (1) complete intersections $A = Q/(f,g)$ where $(Q,\mathfrak n)$ is regular local of dimension three and $f \in \n^2 \setminus \n^3$; (2) one dimensional Cohen–Macaulay quotients of a two dimensional Cohen–Macaulay local ring with pseudo-rational singularity.

Keywords: Hilbert functions, blow-up algebras

Puthenpurakal Tony: On the monotonicity of Hilbert functions. Rend. Sem. Mat. Univ. Padova Electronically published on November 20, 2018. doi: 10.4171/RSMUP/11 (to appear in print)