AI 中文总结
研究离散赋值域上曲线约化类型，通过任意正则模型特殊纤维定义，证明此定义下极小正则模型与极小正则正常交叉模型约化类型相互决定且与低亏格早期分类结果兼容，关键是基于扎里斯基等奇性概念的奇点不变量。
AI 中文摘要
我们提出了一种根据任意正则模型的特殊纤维来定义离散赋值域上曲线约化类型的方法。我们证明，在此定义下，基于极小正则模型的约化类型决定基于极小正则正常交叉模型的约化类型，反之亦然。我们还表明，我们的定义与低亏格下早期的分类结果兼容，即椭圆曲线的柯达依 - 内龙分类以及亏格为2时的上野 - 并川分类结果。我们定义中的关键新元素是特殊纤维上奇点的一个合适不变量，它基于扎里斯基引入的等奇性概念。
英文摘要
We propose a definition of the reduction type of a curve over a discretely valued field in terms of the special fibre of an arbitrary regular model. We show that under this definition, the reduction type in terms of the minimal regular model determines and reduction type in terms of the minimal regular normal crossings model and vice versa. We also show that our definition is compatible with earlier classification results in low genus, namely the Kodaira-Néron classification for elliptic curves and the classification result of Namikawa-Ueno in genus 2. The essential new element in our definition is a suitable invariant of the singularities on the special fibre, building on the notion of equisingularity introduced by Zariski.
Comments30 pages, comments welcome!
