0000000000803119
AUTHOR
C. Mendes De Jesus
showing 3 related works from this author
Bridges, channels and Arnold's invariants for generic plane curves
2002
Abstract We define sums of plane curves that generalize the idea of connected sum and show how Arnol'd's invariants behave with respect to them. We also consider the inverse process of decomposition of a curve and as an application, obtain a new method that reduces considerably the amounts of computation involved in the calculation of Arnold's invariants.
Graphs of stable maps from closed surfaces to the projective plane
2018
Abstract We describe how to attach a weighted graph to each stable map from closed surfaces to projective plane and prove that any weighted graph with non negatively weighted vertices is the graph of some stable map from a closed surface to the projective plane.
Stable maps from surfaces to the plane with prescribed branching data
2007
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 ma…