Alexander-equivalent Zariski pairs of irreducible sextics

TL;DR

This paper constructs the first explicit example of Alexander-equivalent Zariski pairs of irreducible sextic curves, confirming their existence beyond theoretical proof.

Contribution

It provides the first concrete example of Alexander-equivalent Zariski pairs of degree 6 irreducible curves, previously only known to exist theoretically.

Findings

Explicit example of Alexander-equivalent Zariski pairs of sextics provided

Confirms theoretical existence of such pairs with concrete illustration

Advances understanding of curve topology and algebraic geometry

Abstract

The existence of Alexander-equivalent Zariski pairs dealing with irreducible curves of degree 6 was proved by A. Degtyarev. However, up to now, no explicit example of such a pair was available (only the existence was known). In this paper, we construct the first concrete example.