RT Journal Article
T1 Deformation of finite morphisms and smoothing of ropes
A1 Gallego Rodrigo, Francisco Javier
A1 González Andrés, Miguel
A1 Purnaprajna, Bangere P.
AB 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.
PB Cambridge University Press
SN 0010-437X
YR 2008
FD 2008-03-14
LK https://hdl.handle.net/20.500.14352/49667
UL https://hdl.handle.net/20.500.14352/49667
LA eng
DS Docta Complutense
RD 7 may 2024