论文标题
在常规但非平滑整体曲线上
On regular but non-smooth integral curves
论文作者
论文摘要
让$ c $是不完美的字段$ k $的常规几何积分曲线，并假设它承认它是一个非平滑点$ \ mathfrak {p} $，它被视为可分离函数字段$ k（c）| k $的素数，在基地field extement $ \\ overline $ \\ overline $ \\ k} k} {k} k k k（c k k k k k k k k k k k k k k k k k k akectement $ k（c）| k k k k（c ked）在本文中，我们为将$ \ mathfrak {p} $转换为理性点所需的迭代frobenius撤回次数绑定了一个绑定。这提供了一种算法，以计算非平滑点的几何$δ$Δ$ invariants，以及一种构建具有处方$Δ$ invariants的奇异性的纤维的程序。我们表明，在特征2中的界限是锋利的。我们进一步研究了平面投射有理四分之一的铅笔的几何形状，其通用纤维达到了我们的界限。在途中，我们证明了可能具有独立关注的可分离和未分解点的结果。
Let $C$ be a regular geometrically integral curve over an imperfect field $K$ and assume that it admits a non-smooth point $\mathfrak{p}$ which -- seen as a prime of the separable function field $K(C)|K$ -- is non-decomposed in the base field extension $\overline{K} \otimes_K K(C)|\overline{K}$. In this paper we establish a bound for the number of iterated Frobenius pullbacks needed in order to transform $\mathfrak{p}$ into a rational point. This provides an algorithm to compute geometric $δ$-invariants of non-smooth points and a procedure to construct fibrations with moving singularities of prescribed $δ$-invariants. We show that the bound is sharp in characteristic 2. We further study the geometry of a pencil of plane projective rational quartics in characteristic 2 whose generic fibre attains our bound. On our way, we prove several results on separable and non-decomposed points that might be of independent interest.
