Singularidades de aplicações de reflexão

Abstract

In this work, we consider some problems related to germs of reflected graph maps f, from (Cn, 0) to (Cn+1

, 0). A reflected graph map is a particular case of a reflection map, defined as the composition of the map induced by the action of a reflection group G on Cn+1 with an embedding of Cn into Cn+1

. In this work, we present a description of the presentation matrix of f⋆On as an On+1-module via f, in terms of the action of the associated reflection group G. As a consequence, we also provide a defining equation for the image of f, again in terms of the action of G. Moreover, we present upper and lower bounds for the multiplicity of the image of f, along with some applications. Finally, we introduce a new class of map germs, called “2m-dihedral map germs” and we apply the results obtained to study this class of maps.