Discriminant and Singularities of Logarithmic Gauss Map, Examples and Application

Details Discriminant and Singularities of Logarithmic Gauss Map, Examples and Application Discriminant and Singularities of Logarithmic Gauss Map, Examples and Application

2012-02-21

arxiv.org/abs/1202.4659v1

Mathematics

Complex Variables

12 pages, 2 figures

Scientific paper

The study of hypersurfaces in a torus leads to the beautiful zoo of amoebas and their contours, whose possible configurations are seen from combinatorial data. There is a deep connection to the logarithmic Gauss map and its critical points. The theory has a lot of applications in many directions. In this report we recall basic notions and results from the theory of amoebas, show some connection to algebraic singularity theory and discuss some consequences from the well known classification of singularities to this subject. Moreover, we have tried to compute some examples using the computer algebra system SINGULAR and discuss different possibilities and their effectivity to compute the critical points. Here we meet an essential obstacle: Relevant examples need real or even rational solutions, which are found only by chance. We have tried to unify different views to that subject.

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