Gallego Rodrigo, Francisco JavierGonzález Andrés, MiguelPurnaprajna, Bangere P.2023-06-202023-06-202008-03-140010-437X10.1112/S0010437X07003326https://hdl.handle.net/20.500.14352/49667In this paper we prove that most ropes of arbitrary multiplicity supported on smooth curves can be smoothed. By a rope being smoothable we mean that the rope is the flat limit of a family of smooth, irreducible curves. To construct a smoothing, we connect, on the one hand, deformations of a finite morphism to projective space and, on the other hand, morphisms from a rope to projective space. We also prove a general result of independent interest, namely that finite covers onto smooth irreducible curves embedded in projective space can be deformed to a family of 1 : 1 maps. We apply our general theory to prove the smoothing of ropes of multiplicity 3 on P1. Even though this paper focuses on ropes of dimension 1, our method yields a general approach to deal with the smoothing of ropes of higher dimension.engjournal articlehttp://journals.cambridge.org/action/displayJournal?jid=COMopen access512.7Degenerations of curvesMultiple structuresDeformations of morphismsGeometria algebraica1201.01 Geometría Algebraica