ON THE LINEAR-TYPE PROPERTY OF THE JACOBIAN IDEAL OF AFFINE PLANE CURVES

Abstract

An ideal $I$ in a Noetherian ring $R$ is called of linear type if the Rees algebra of $I$ is isomorphic to the symmetric algebra of $I$. We prove that the Jacobian ideal of any reduced plane curve with singular points of multiplicity $2$ is of linear type. We characterize plane curves with singular points of multiplicity $3$ whose Jacobian ideal is of linear type.