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摘要翻译：
设x/s是离散赋值环谱上亏格g的超椭圆曲线。在X/S上有两个基本的数值不变量：X/S的超椭圆判别的值和X/S的Mumford判别的值（等价为Artin导体）。对于特征为0的留数场，以及对于x/s半可态，这些不变量满足某些不等式。在半稳态情况下，我们用由特殊光纤上Weierstrass点分布确定的交集理论数据证明了两个不变量之间的精确关系式。我们还证明了数域上任意曲线稳定支撑高度的精确公式，其中包含了与其Weierstrass点相关的局部贡献。
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英文标题：
《Local invariants attached to Weierstrass points》
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作者：
Robin de Jong
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最新提交年份：
2012
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
Let X/S be a hyperelliptic curve of genus g over the spectrum of a discrete valuation ring. Two fundamental numerical invariants are attached to X/S: the valuation of the hyperelliptic discriminant of X/S, and the valuation of the Mumford discriminant of X/S (equivalently, the Artin conductor). For a residue field of characteristic 0 as well as for X/S semistable these invariants are known to satisfy certain inequalities. We prove an exact formula relating the two invariants with intersection theoretic data determined by the distribution of Weierstrass points over the special fiber, in the semistable case. We also prove an exact formula for the stable Faltings height of an arbitrary curve over a number field, involving local contributions associated to its Weierstrass points.
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PDF链接：
https://arxiv.org/pdf/0710.5464
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