Examples of strong Ziegler pairs of conic-line arrangements of degree 7 and 8

2025/09/10 by Shinzo Bannai, Bannai, Shinzo, Hiro‐o Tokunaga +1
Mathematics · #Algebraic Geometry and Number Theory #Advanced Combinatorial Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2509.08403

Abstract

A pair of plane curves with the same combinatorics is said to be (a) a Zariski pair if the plane curves have different embedded topology, and (b) a strong Ziegler pair if their Milnor algebra are not isomorphic. We show that some examples of Zariski pairs are also strong Ziegler pairs.

Citations

• On plus-one generated arrangements of plane conics
• A new hierarchy for complex plane curves
• The realization spaces of certain conic-line arrangements of degree 7
• Singular plane curves: freeness and combinatorics
• Poncelet's closure theorem and the embedded topology of conic-line arrangements
• The realization space of a certain conic line arrangement of degree 7 and a π₁-equivalent Zariski pair
• Zariski pairs of conic-line arrangements of degrees 7 and 8 via fundamental groups
• Trisections on Certain Rational Elliptic Surfaces and Families of Zariski Pairs Degenerating to the same Conic-line Arrangement
• Torsion divisors of plane curves and Zariski pairs
• Geometry of bisections of elliptic surfaces and Zariski N-plets II
• On the topology of arrangements of a cubic and its inflectional tangents
• Cohomology algebra of plane curves, weak combinatorial type, and formality

Related

• Weak Ziegler pairs of conic-line arrangements with ordinary singularities
• Zariski pairs of conic-line arrangements of degrees 7 and 8 via fundamental groups
• A note on Zariski pairs
• Zariski pairs of conic-line arrangements with a unique conic
• The realization space of a certain conic line arrangement of degree 7 and a π₁-equivalent Zariski pair