Classification of the fundamental groups of join-type curves of degree seven

Abstract

We compute the fundamental groups π₁(ℙ² \ C) for all complex curves C of degree 7 defined by an equation of the formwhere ∑^ℓ_j=1 ν_j = ∑^m_i=1 λ_i is the degree of the curve, c ∈ ℝ \ {0}, and β₁,…,β_ℓ (respectively α₁,…,α_m) mutually distinct real numbers.