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Título:
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Deformation of finite morphisms and smoothing of ropes
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Autores:
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Gallego Rodrigo, Francisco Javier ;
González Andrés, Miguel ;
Purnaprajna, Bangere P.
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Tipo de documento:
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texto impreso
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Editorial:
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Cambridge University Press, 2008-03-14
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Dimensiones:
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application/pdf
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Nota general:
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info:eu-repo/semantics/openAccess
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Idiomas:
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Geometria algebraica
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Tipo = Artículo
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Resumen:
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In 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.
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En línea:
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https://eprints.ucm.es/id/eprint/12607/1/2008deformation.pdf
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