Mounir Nisse, Texas A&M University, USA

The k-Convexity of the amoeba complement and the generalized order map

Abstract

Amoebas are the images under the logarithmic map of algebraic (or analytic) varieties of the complex algebraic torus. They inherit some algebraic, geometric, and topological properties of the variety itself. A global statement generalizing convexity of amoeba complement components was found by André  Henriques, and he proved a weaker version of this property for the complement of amoebas. We show a stronger version which complete the generalization of the k-convexity of the amoeba complement in higher codimension. Moreover, we define the generelized order maping in higher codimension, which is already well defined for hypersurface by Passare and Tsikh. (This is a joint work with Frank Sottile.)