On the Artal--Carmona--Cogolludo construction

Abstract

We derive explicit defining equations for a number of irreducible maximizing plane sextics with double singular points only. For most real curves, we also compute the fundamental group of the complement; all groups found are abelian. As a by-product, examples of Zariski pairs in the strongest possible sense are constructed.

Revised version prepared for publication, with newly found results incorporated

References in corpus (2)

• Oka's conjecture on irreducible plane sextics
• On plane sextics with double singular points

Cited by in corpus (2)

• Geography of irreducible plane sextics
• Parametric equations of plane sextic curves with a maximal set of double points