Given an irreducible surface germ (X, 0) ⊂ (ℂ3, 0) with a one-dimensional singular setΣ, we denote byδ1(X, 0) the delta invariant of a transverse slice. We show thatδ1(X, 0) ≥m0(Σ, 0), with equality if and only if (X, 0) admits a corank 1 parametrizationf:(ℂ2, 0) → (ℂ3, 0) whose only singularities outside the origin are transverse double points and semi-cubic cuspidal edges. We then use the local Euler obstruction Eu(X, 0) in order to characterize those surfaces that have finite codimension

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... respect to-equivalence or as a frontal-type singularity.