Amoebas of half-dimensional varieties

Grigory Mikhalkin

Amoebas of half-dimensional varieties

Algebraic Geometry 2015-09-01 v2

Authors: Grigory Mikhalkin

Abstract

An $n$ -dimensional algebraic variety in $({\mathbb C}^\times)^{2n}$ covers its amoeba as well as its coamoeba generically finite-to-one. We provide an upper bound for the volume of these amoebas as well as for the number of points in the inverse images under the amoeba and coamoeba maps.

Keywords

intrinsic volumes of polytopes simplicial volume abelian varieties

Cite

@article{arxiv.1412.4658,
  title  = {Amoebas of half-dimensional varieties},
  author = {Grigory Mikhalkin},
  journal= {arXiv preprint arXiv:1412.4658},
  year   = {2015}
}

Comments

In memory of Mikael Passare. Changes in the 2nd version: misprints corrected, references expanded

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