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Weak Ziegler pairs of conic-line arrangements with ordinary singularities

Magdalena Lampa-Baczyńska, Daniel Wojcik

Abstract

In the present note we focus on conic line arrangements in the plane with quasihomogeneous ordinary singularities from the perspective of weak Ziegler pairs. The foundations of this article come from an active area of research devoted to the freeness and nearly freeness of curve arrangements in the complex projective plane and the socalled Numerical Terao s Conjecture. This conjecture boils down to a very fundamental problem in combinatorial algebraic geometry, namely whether the weak combinatorics of a given arrangement determines the freeness.

Weak Ziegler pairs of conic-line arrangements with ordinary singularities

Abstract

In the present note we focus on conic line arrangements in the plane with quasihomogeneous ordinary singularities from the perspective of weak Ziegler pairs. The foundations of this article come from an active area of research devoted to the freeness and nearly freeness of curve arrangements in the complex projective plane and the socalled Numerical Terao s Conjecture. This conjecture boils down to a very fundamental problem in combinatorial algebraic geometry, namely whether the weak combinatorics of a given arrangement determines the freeness.
Paper Structure (2 sections, 10 equations, 2 figures)

This paper contains 2 sections, 10 equations, 2 figures.

Table of Contents

  1. Data availability statement
  2. Acknowledgement

Figures (2)

  • Figure 1: Geometric presentation of arrangement $\mathcal{CL}_{1}$.
  • Figure 2: Geometric presentation of arrangement $\mathcal{CL}_{2}$.

Theorems & Definitions (9)

  • Definition 1
  • Conjecture 2: Numerical Terao's Conjecture
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Definition 7: Weak Ziegler pair
  • Remark 8
  • proof