%0 Journal Article
%A Gallego Rodrigo, Francisco Javier
%A González Andrés, Miguel
%A Purnaprajna, Bangere P.
%T Deformation of finite morphisms and smoothing of ropes
%D 2008
%@ 0010-437X
%U https://hdl.handle.net/20.500.14352/49667
%X In this paper we prove that most ropes of arbitrary multiplicity supported on smoothcurves 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.
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