On intrinsic negative curves

Abstract

Let $\mathbb{K}$ be an algebraically closed field of characteristic $0$. A curve of $({\mathbb{K}}^{\ast }{)}^2$ 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.

Final version, minor changes