On the monotonicity of Hilbert functions

  • Tony J. Puthenpurakal

    Indian Institute of Technology Bombay, Mumbai, India
On the monotonicity of Hilbert functions cover
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In this paper we show that a large class of one-dimensional Cohen–Macaulay local rings (A,m)(\mathcal A,\mathfrak m) has the property that if MM is a maximal Cohen–Macaulay AA-module then the Hilbert function of MM (with respect to m\mathfrak m) is non-decreasing. Examples include (1) complete intersections A=Q/(f,g)A = Q/(f,g) where (Q,n)(Q,\mathfrak n) is regular local of dimension three and fn2n3f \in \mathfrak n^2 \setminus \mathfrak n^3; (2) one dimensional Cohen–Macaulay quotients of a two dimensional Cohen–Macaulay local ring with pseudo-rational singularity.

Cite this article

Tony J. Puthenpurakal, On the monotonicity of Hilbert functions. Rend. Sem. Mat. Univ. Padova 141 (2019), pp. 1–8

DOI 10.4171/RSMUP/11