Zariski $k$-plets via dessins d'enfants

Abstract

We construct exponentially large collections of pairwise distinct equisingular deformation families of irreducible plane curves sharing the same sets of singularities. The fundamental groups of all curves constructed are abelian.

Final version accepted for publication

References in corpus (4)

• Oka's conjecture on irreducible plane sextics
• Non-homeomorphic conjugate complex varieties
• Zariski Pairs on sextics II
• On arithmetic Zariski pairs in degree 6