On intrinsic negative curves

Abstract

Let $\mathbb K$ be an algebraically closed field of characteristic $0$. A curve of $(\mathbb K^*)^2$ arising from a Laurent polynomial in two variables is {\em intrinsic negative} if its tropical compactification has negative self-intersection. The aim of this note is to start a systematic study of these curves and to relate them with the problem of computing Seshadri constants of toric surfaces.