A generalisation of the toric resolution of curves

Abstract

Let $k$ be a perfect field and let $C_0:f=0$ be a smooth curve in the torus ${\mathbb{G}}_{m,k}^2$. Let ${\mathbb{T}}_{\hat{I}}”$ be the toric variety associated to the Newton polygon of $f$. Extending the toric resolution of $C_0$ on ${\mathbb{T}}_{\hat{I}}”$, we construct an explicit model over $k$ of the smooth completion of $C_0$. Such a model exists for any smooth projective curve and can be described via a combinatorial algorithm using an iterative construction of Newton polygons.

43 pages. Comments are welcome