Silviu Bălănescu,
Mircea Cimpoeaş
and Christian Krattenthaler
On the Hilbert depth of monomial ideals
(20 pages)
Abstract.
Let S=K[x1,...,xn]
be the ring of polynomials over a field K.
Given two monomial ideals 0 ⊂ I ⊊ J ⊂ S,
we present a new method to compute
the Hilbert depth of J/I. As an application, we show that if
u ∈ S is a monomial regular of S/I, then
qdepth(S/I) ≥ qdepth(S/(I,u)) ≥
qdepth(S/I)-1.
Also, we reprove the formula for the Hilbert depth of a squarefree Veronese ideal.
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