Amoebas and coamoebas of linear spaces

2012/05/12 by Nisse, Mounir, Passare, Mikael
#14T05 #32A60 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1205.2808

Abstract

We give a complete description of amoebas and coamoebas of k-dimensional very affine linear spaces in (ℂ^*)ⁿ. This include an upper bound of their dimension, and we show that if a k-dimensional very affine linear space in (ℂ^*)ⁿ is generic, then the dimension of its (co)amoeba is equal to min \ 2k, n\. Moreover, we prove that the volume of its coamoeba is equal to π^2k. In addition, if the space is generic and real, then the volume of its amoeba is equal to \fracπ^2k2^k.

Related

• The amoeba dimension of a linear space
• Amoebas of half-dimensional varieties
• Analytic varieties with finite volume amoebas are algebraic
• A Ronkin type function for coamoebas
• Generalized amoebas for subvarieties of GL_n(ℂ)