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Generalized logarithmic Gauss map and its relation to (co)amoebas
Author(s) -
Madani Farid,
Nisse Mounir
Publication year - 2013
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200204
Subject(s) - mathematics , logarithm , gauss map , hypersurface , codimension , torus , pure mathematics , algebraic number , variety (cybernetics) , algebraic variety , gauss , mathematical analysis , geometry , statistics , physics , quantum mechanics
We define the generalized logarithmic Gauss map for algebraic varieties of the complex algebraic torus of any codimension. Moreover, we describe the set of critical points of the logarithmic mapping restricted to our variety, and we show an analogous of Mikhalkin's result on the critical points of the logarithmic map restricted to a hypersurface.