Let $K$ be a field complete with respect to an absolute value associated to a nontrivial discrete valuation. Let $K^{\circ}$ be the ring of integers. Let $X$ be a proper curve over $K$. A semi-stable model of $X$ is a flat proper regular scheme ${\mathcal{X}}$ of finite type over $\operatorname{Spec}(K^{\circ})$ with an isomorphism $X\to{\mathcal{X}}_{\eta}$, such that the special fibre ${\mathcal{X}}_{o}$ is a reduced normal crossing divisor.