On Intrinsic Negative Curves

Abstract

Let 𝕂 be an algebraically closed field of characteristic 0. A curve of (𝕂∗)2 arising from a Laurent polynomial in two variables is 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.