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

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 cas...

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Hauptverfasser:	Nejad, Abbas Nasrollah, Shahidi, Zahra
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Schlagworte:	Mathematics - Algebraic Geometry Mathematics - Commutative Algebra
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description	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.
doi_str_mv	10.48550/arxiv.1906.00626
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title	The module of Valabrega-Valla of the Jacobian ideal of points in projective plane
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