5 papers
Free plane curves with a linear Jacobian syzygy
Valentina Beorchia, Matteo Gallet, Alessandro Logar
The study of planar free curves is a very active area of research, but a structural study of such a class is missing. We give a complete classification of the possible generators o…
Weak Lefschetz property of equigenerated complete intersections. Applications
Valentina Beorchia, Rosa Maria Miró-Roig
In this paper, we prove that any Artinian complete intersection homogeneous ideal in generated by forms of degree satisfies the weak Lefschet…
Quasi-homogeneous singularities of projective hypersurfaces and Jacobian syzygies
Aline V. Andrade, Valentina Beorchia, Alexandru Dimca +1
We prove an unexpected general relation between the Jacobian syzygies of a projective hypersurface with only isolated singularities and the nature of its si…
Eigenpoint collinearities of plane cubics
Valentina Beorchia, Matteo Gallet, Alessandro Logar
Given a ternary homogeneous polynomial, the fixed points of the map from to itself defined by its gradient are called its eigenpoints. We focus on cubic polynomials,…
A characterization of quasi-homogeneous singularities of free and nearly free plane curves
Aline V. Andrade, Valentina Beorchia, Rosa M. Miró-Roig
The goal of this paper is to establish a new characterization of quasi-homogeneous isolated singularities of free curves and nearly free curves in . Th…