Studia Scientiarum Mathematicarum Hungarica 51 (1), 92–104 (2014) DOI: 10.1556/SScMath.51.2014.1.1267 A CLASSIFIER FOR SIMPLE SPACE CURVE SINGULARITIES FAIRA KANWAL JANJUA 1 and GERHARD PFISTER 2 1 Abdus Salam School of Mathematical Sciences, GC University, Lahore 68-B, New Muslim Town, Lahore 54600, Pakistan e-mail: fairakanwaljanjua@gmail.com 2 Department of Mathematics, University of Kaiserslautern, Erwin-Schr¨ odinger-Str., 67663 Kaiserslautern, Germany e-mail: pfister@mathematik.uni-kl.de Communicated by A. N´ emethi (Received July 22, 2013; accepted December 17, 2013) Abstract The classification of Bruce and Gaffney respectively Gibson and Hobbs for simple plane curve singularities respectively simple space curve singularities is characterized in terms of invariants. This is the basis for the implementation of a classifier in the computer algebra system singular. 1. Introduction The germ of a space curve is given by a germ of an analytic map f : (C, 0) → (C n , 0). Simple singularities of curves have been classified by Bruce and Gaffney in the case n = 2 and Gibson and Hobbs for the case n = 3. We will describe the implementation of a classifier in singular for simple curve singularities in case n ≦ 3. Instead of considering the germ f :(C, 0) → (C n , 0) we may as well con- sider the corresponding C-algebra morphism f ∗ : C[[x 1 ,...,x n ]] → C[[t]]. Let A n := {f : C[[x 1 ,...,x n ]] → C[[t]] | dim C C[[t]]/ Im(f ) < ∞}. The group A n := Aut C C[[x 1 ,...,x n ]] × Aut C C[[t]] acts on A n by (ϕ,ψ)(f )= ψ ◦ f ◦ ϕ −1 . Definition 1.1. f is called A-equivalent to g if f,g are in the same orbit of A n . Since a C-algebra morphism f : C[[x 1 ,...,x n ]] → C[[t]] is determined 2010 Mathematics Subject Classification. Primary 14Q05, 14H20. Key words and phrases. A-equivalence, irreducible space curve singularities, simple singularities, singular. 0081–6906/$ 20.00 c ⃝ 2014 Akad´ emiai Kiad´ o, Budapest