• search hit 12 of 45
Back to Result List

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 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.

Export metadata

Additional Services

Search Google Scholar
Metadaten
Author: Bernd Martin, Dimitry Pochekutov
ISSN:1997-1397
Title of the source (English):Journal of Siberian Federal University, Mathematik & Physics
Document Type:Scientific journal article peer-reviewed
Language:English
Year of publication:2013
Contributing Corporation:Siberian Federal University
Tag:logarithmic Gauss map, singularities, discriminant, asymptotics, hypersurface amoeba
Volume/Year:6
Issue number:1
First Page:74
Last Page:85
Faculty/Chair:Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Algorithmische Mathematik
Institution name at the time of publication:Fakultät für Mathematik, Naturwissenschaften und Informatik (eBTU) / LS Mathematik, insbesondere Algebra und Geometrie
Einverstanden ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.