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arXiv · 1906.00626

The module of Valabrega-Valla of the Jacobian ideal of points in projective plane

Abbas Nasrollah Nejad·Zahra Shahidi
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Abstract

The module of Valabrega-Valla of the Jacobian ideal of a reduced projective variety $V$ is the torsion of the Aluffi algebra. One considers the problem of its vanishing in the case of where $V$ is a reduced set of points in the projective plane. It is shown that the module is nonzero for several cases of a special configuration class therein -- called $(s-r)$-{fold collinear configuration}. A complete classification of types is given for $5$ and $6$ points in regard to this problem.

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Abbas Nasrollah Nejad, Zahra Shahidi. 2019-06-03. The module of Valabrega-Valla of the Jacobian ideal of points in projective plane. https://arxiv.org/abs/1906.00626

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