Graphs of stable maps from closed orientable surfaces to the 2-sphere

D. Hacon, C. Mendes de Jesus and M.C. Romero Fuster

Journal of Singularities
volume 2 (2010), 67-80
Proceedings of Singularities in Aarhus, August 2009

Received: 28 December 2009.

DOI: 10.5427/jsing.2010.2e

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Abstract:

We prove that any bipartite weighted graph can be associated to some stable map from a closed orientable surface to the sphere and obtain necessary and sufficient conditions on a graph to be attached to a fold map of a given degree.

Keywords:

Stable maps, graphs, branch sets, degree

Mathematical Subject Classification:

57R45, 57M15, 57R65

Author(s) information:

D. Hacon	C. Mendes de Jesus	M.C. Romero Fuster
Dep. de Matemática	Dep. de Matemática	Dep. Geometria i Topologia
PUC-Rio	UFV	Facultat de Matemàtiques
22453-900 Rio de Janeiro-RJ	36570-000 - Viçosa - MG	46100 - Universitat de València
email: derek@mat.puc-rio.br	email: cmendes@ufv.br	email: carmen.romero@uv.es