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Paper IPM / M / 15323  


Abstract:  
A pair of ideals J ⊆ I ⊆ R has been called Aluffi torsionfree if the Aluffi algebra of I/J is isomorphic with the corresponding Rees algebra. We give necessary and sufficient conditions for the Aluffi torsionfree property in terms of the first syzygy module of the form ideal J^{*} in the associated graded ring of I. For two pairs of ideals J_{1},J_{2} ⊆ I such that J_{1}−J_{2} ∈ I^{2}, we prove that if one pair is Aluffi torsionfree the other one is so if and only if the first syzygy modules of J_{1} and J_{2} have the same form ideals. We introduce the notion of strongly Aluffi torsionfree ideals and present some results on these ideals.
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