Mounir Nisse: Minimal varieties and (co)amoebas

Abstrac: First, we observe that the (co)amoeba of a generic analytic variety in the complex algebraic torus of dimension at least the double of the complex dimension of the variety itself is a minimal variety (i.e. the mean curvature vanishes). Using this observation, we show some geometric and topological properties of the complement of (co)amoebas of varieties of higher codimension. Moreover, we give a necessary condition on a variety to have a (co)amoeba of minimal dimension. Part of this talk is a joint work with Frank Sottile.