Analytic varieties with finite volume amoebas are algebraic

Farid Madani; Mounir Nisse

Analytic varieties with finite volume amoebas are algebraic

Algebraic Geometry 2011-08-09 v1 Complex Variables

Authors: Farid Madani , Mounir Nisse

Abstract

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 $n\geq 2k$ , we show that $V$ is algebraic if and only if the volume of its amoeba is finite. In this precise case, we establish a comparison theorem for the volume of the amoeba and the coamoeba. Examples and applications to the $k-$ linear spaces will be given.

Keywords

amoeba volume analytic variety algebraic torus coamoeba k-linear space

Cite

@article{arxiv.1108.1444,
  title  = {Analytic varieties with finite volume amoebas are algebraic},
  author = {Farid Madani and Mounir Nisse},
  journal= {arXiv preprint arXiv:1108.1444},
  year   = {2011}
}

Comments

13 pages, 2 figures

Analytic varieties with finite volume amoebas are algebraic

Abstract

Keywords

Cite

Comments

Related papers