The amoeba 
of an algebraic variety 
is the image of 
under the map
![Log(z_1,...,z_n)=[ln|z_1|,...,ln|z_n|].](/images/equations/Amoeba/NumberedEquation1.svg) |
Here 
denotes the componentwise log-absolute-value
map, not the complex logarithm. Thus 
is a subset of 
. The fiber over 
is the 
-torus
 |
Consequently, 
forgets the complex argument of each coordinate
and retains only the logarithm of its complex
modulus. The corresponding image under the coordinatewise argument map is the coamoeba of 
. For a Laurent polynomial 
, the connected
components of the complement set of the amoeba
of 
are convex.
Amoebas connect the geometry of complex varieties
with convex geometry and tropical
geometry. The mathematical literature generally uses the plural "amoebas"
(e.g., Forsberg et al. 2000), while "amoebae" is common for the
biological organisms.
