On the monotonicity of Hilbert functions
Puthenpurakal, Tony1
1 Indian Institute of Technology Bombay, Mumbai, India
Rendiconti del Seminario Matematico della Università di Padova, Tome 141 (2019), pp. 1-8.
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In this paper we show that a large class of one-dimensional Cohen–Macaulay local rings (𝒜,𝔪) has the property that if M is a maximal Cohen–Macaulay A-module then the Hilbert function of M (with respect to 𝔪) is non-decreasing. Examples include (1) complete intersections A=Q/(f,g) where (Q,𝔫) is regular local of dimension three and f∈𝔫 2 ∖𝔫 3 ; (2) one dimensional Cohen–Macaulay quotients of a two dimensional Cohen–Macaulay local ring with pseudo-rational singularity.

Publié le :
DOI : 10.4171/RSMUP/11
Classification : 13, 00
Mots-clés : Hilbert functions, blow-up algebras
Puthenpurakal, Tony 1

1 Indian Institute of Technology Bombay, Mumbai, India 
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Puthenpurakal, Tony. On the monotonicity of Hilbert functions. Rendiconti del Seminario Matematico della Università di Padova, Tome 141 (2019), pp. 1-8. doi : 10.4171/RSMUP/11. http://archive.numdam.org/articles/10.4171/RSMUP/11/

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