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

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.