Models and integral differentials of hyperelliptic curves

Pub Date : 2024-03-18 DOI:10.1017/s001708952400003x

Simone Muselli

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引用次数: 0

Abstract

Let

$C\; : \;y^2=f(x)$

be a hyperelliptic curve of genus

$g\geq 1$

, defined over a complete discretely valued field

$K$

, with ring of integers

$O_K$

. Under certain conditions on

$C$

, mild when residue characteristic is not

$2$

, we explicitly construct the minimal regular model with normal crossings

$\mathcal{C}/O_K$

$C$

. In the same setting we determine a basis of integral differentials of

$C$

, that is an

$O_K$

-basis for the global sections of the relative dualising sheaf

$\omega _{\mathcal{C}/O_K}$

查看原文

超椭圆曲线的模型和积分微分

让 $C\; ：\y^2=f(x)$是一条属$g\geq 1$的超椭圆曲线，定义在一个完整的离散值域$K$上，其整数环为$O_K$。在 $C$ 的某些条件下 , 当残差特征不为 2$ 时 , 我们明确地构造了具有法线交叉 $\mathcal{C}/O_K$ 的最小正则模型 .在同样的背景下，我们确定了$C$的积分微分基础，即相对对偶化剪$\omega _{\mathcal{C}/O_K}$的全局截面的$O_K$基础。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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