The Aluffi algebra of the Jacobian of points in projective space: Torsion-freeness

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The algebra in the title has been introduced by P. Aluffi. Let J⊂I be ideals in the commutative ring R. The (embedded) Aluffi algebra of I on R/J is an intermediate graded algebra between the symmetric algebra and Rees Algebra of the ideal I/J over R/J. A pair of ideals has been dubbed an Aluffi torsion-free pair if the surjective map of the Aluffi algebra of I/J onto the Rees algebra of I/J is injective. In this paper we focus on the situation where J is the ideal of points in general linear position in projective space and I is its Jacobian ideal.