Conic-line arrangements in the complex projective plane

Abstract

The main goal of this note is to begin a systematic study on conic-line arrangements in the complex projective plane. We show a de Bruijn-Erdős-type inequality and Hirzebruch-type inequality for a certain class of conic-line arrangements having ordinary singularities. We will also study, in detail, certain conic-line arrangements in the context of the geography of log-surfaces and free divisors in the sense of Saito.

17 pages, 2 figures. Version 3.0, this is the version incorporating referee's remarks

References in corpus (1)

• Abstract configurations in algebraic geometry

Cited by in corpus (8)

• On conic-line arrangements with nodes, tacnodes, and ordinary triple points
• Maximizing curves viewed as free curves
• $\mathcal{Q}$-conic arrangements in the complex projective plane
• On free and nearly free arrangements of conics admitting certain $\mathrm{ADE}$ singularities
• Zariski pairs of conic-line arrangements of degrees 7 and 8 via fundamental groups
• Algebraic properties of binomial edge ideals of Levi graphs associated with curve arrangements
• Bounds for characteristic numbers of conic-line arrangements in the plane
• Pencils of Conic-Line Curves