On free arrangements of three conics

We give a complete classification of free arrangement of three smooth conics on complex projective plane admitting only ${\rm ADE}$ singularities and $J_{2,0}$ singularities.

💡 Research Summary

The paper investigates free arrangements of three smooth conics in the complex projective plane ℙ²(ℂ) under the restriction that all singularities are either of ADE type or the quasi‑homogeneous J₂,₀ type. A free arrangement is defined as one whose Jacobian module of the defining homogeneous polynomial is a free module over the coordinate ring S=ℂ