A discriminant and an upper bound for ! 2 for hyperelliptic arithmetic surfaces
A discriminant and an upper bound for ! 2 for hyperelliptic arithmetic surfaces
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的判别式和上限！
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发表时间：
1998
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通讯作者：
I. Kausz
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作者：
I. Kausz
定义域K上亏格为g的超椭圆曲线X的自然判别式为X上整体微分形式向量空间的最大外积的第（8g+ 4）次张量积的标准元.如果v是K上的离散赋值，且X在v处有半稳定约化，则我们根据X在v上约化的几何关系计算判别式在v处的消失阶.作为应用，我们找到了半稳定超椭圆算术曲面上相对对偶层的Arakelov自交的一个上界。数学学科分类（1991）：11G30，14G40，14H10。
We define a natural discriminant for a hyperelliptic curve X of genusg over a fieldK as a canonical element of the (8g+ 4)th tensor power of the maximal exterior product of the vectorspace of global differential forms onX. If v is a discrete valuation on K andX has semistable reduction at v, we compute the order of vanishing of the discriminant at v in terms of the geometry of the reduction ofX overv. As an application, we find an upper bound for the Arakelov self-intersection of the relative dualizing sheaf on a semistable hyperelliptic arithmetic surface. Mathematics Subject Classifications ( 1991):11G30, 14G40, 14H10.