$\mathcal{Q}$-conic arrangements in the complex projective plane

Abstract

We study the geometry of $\mathcal{Q}$-conic arrangements in the complex projective plane. These are arrangements consisting of smooth conics and they admit certain quasi-homogeneous singularities. We show that such $\mathcal{Q}$-conic arrangements are never free. Moreover, we provide combinatorial constraints of the weak combinatorics of such arrangements.

Version 2.0, 9 pages

References in corpus (2)

• On conic-line arrangements with nodes, tacnodes, and ordinary triple points
• On plane conic arrangements with nodes and tacnodes

Cited by in corpus (4)

• Freeness of arrangements of lines and one conic with ordinary quasi-homogeneous singularities
• On free and nearly free arrangements of conics admitting certain $\mathrm{ADE}$ singularities
• Singular plane curves: freeness and combinatorics
• Deletion-addition of a smooth conic for free curves