KÄHLER DIFFERENTIAL MODULES AND CONFIGURATIONS OF POINTS IN \(\mathbb{P}^2\)

Abstract

Given a finite set of points in the projective plane, we use the module of Kähler differentials to investigate the configurations of these points. More precisely, depending on the values of the Hilbert function of the module of Kähler differential 3-forms, we determine whether the set of points lies on a nonsingular conic, on two different lines, or on a single line.

Keywords

• configuration of points
• finite set of points
• hilbert function
• kähler differential module.