Use este identificador para citar ou linkar para este item: https://locus.ufv.br//handle/123456789/22432
Tipo: Artigo
Título: Stable maps from surfaces to the plane with prescribed branching data
Autor(es): Jesus, C. Mendes de
Hacon, D.
Fuster, M.C. Romero
Abstract: We consider the problem of constructing stable maps from surfaces to the plane with branch set a given set of curves immersed (except possibly with cusps) in the plane. Various constructions are used (1) piecing together regions immersed in the plane (2) modifying an existing stable map by a sequence of codimension one transitions (swallowtails etc) or by surgeries. In (1) the way the regions are pieced together is described by a bipartite graph (an edge C* corresponds to a branch curve C with the vertices of C* corresponding to the two regions containing C). We show that any bipartite graph may be realized by a stable map and we consider the question of realizing graphs by fold maps (i.e. maps without cusps). For example, using Arnol'd's classification of immersed curves, we list all branch sets with at most two branch curves and four double points realizable by planar fold maps of the torus.
Palavras-chave: Stable maps from surfaces
Plane
Editor: Topology and its Applications
Tipo de Acesso: Open Access
URI: http://dx.doi.org/10.1016/j.topol.2006.04.005
http://www.locus.ufv.br/handle/123456789/22432
Data do documento: 1-Jan-2007
Aparece nas coleções:Artigos

Arquivos associados a este item:
Arquivo Descrição TamanhoFormato 
artigo.pdftexto completo536,6 kBAdobe PDFVisualizar/Abrir


Os itens no repositório estão protegidos por copyright, com todos os direitos reservados, salvo quando é indicado o contrário.