Quasi-homogeneous singularities of plane curves

Abstract: This talk aims to present the new criteria to characterize quasi-homogeneous isolated singularities of projective plane curves. The criterion depends on the first syzygy matrix associated with the Jacobian ideal of the plane curve. Our methods rely on geometric techniques, particularly the study of the polar map and the surface obtained as the closure of its graph.

This is a joint work with Valentina Beorchia (Universidà di Trieste/Italy) and Rosa Maria Miró-Roig (Universidad de Barcelona/Spain).