论文标题
曲线曲折分辨率的概括
A generalisation of the toric resolution of curves
论文作者
论文摘要
令$ k $为一个完美的字段，让$ c_0：f = 0 $为圆环$ \ mathbb {g} _ {m，k}^2 $中的平滑曲线。令$ \ mathbb {t}_δ$为与$ f $的牛顿多边形相关的复合品种。在$ \ mathbb {t}_δ$上扩展了$ c_0 $的曲折分辨率，我们在$ c_0 $的平滑完成$ k $上构建了一个显式模型。对于任何平滑的投影曲线，都存在这样的模型，可以使用牛顿多边形的迭代结构通过组合算法来描述。
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 $\mathbb{T}_Δ$ be the toric variety associated to the Newton polygon of $f$. Extending the toric resolution of $C_0$ on $\mathbb{T}_Δ$, 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.
