Analytic varieties with finite volume amoebas are algebraic

Zusammenfassung

In this paper, we study the amoeba volume of a given k-dimensional generic analytic variety V of the complex algebraic torus (C*)(n). When n >= 2k, we show that V is algebraic if and only if the volume of its amoeba is finite. Moreover, in this case, we establish a comparison theorem for the volume of the amoeba and the coamoeba. Examples and applications to the k-dimensional affine linear spaces are also given.