Discriminant and Singularities of Logarithmic Gauss Map, Examples and Application
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...
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| Main Authors | , |
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| Format | Journal Article |
| Language | English |
| Published |
21.02.2012
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| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.1202.4659 |
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| Summary: | 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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| DOI: | 10.48550/arxiv.1202.4659 |