The probability that a complete intersection is smooth
The probability that a complete intersection is smooth
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完整交叉路口平滑的概率
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
K. Kedlaya
中科院分区：
文献类型：
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作者：
A. Bucur;K. Kedlaya
给定有限域上射影空间的平滑子方案，我们计算其与固定数量的大度超曲面部分的交集在预期维度上平滑的概率。这概括了单个超曲面的情况，这是由 Poonen 提出的。我们使用这个结果给出这样一个完整交叉点的有理点数量的概率模型。一个有点令人惊讶的推论是，射影 3 空间中两个表面的随机平滑交线上的有理点数量严格小于射影线上的点数量。
Given a smooth subscheme of a projective space over a finite field, we compute the probability that its intersection with a fixed number of hypersurface sections of large degree is smooth of the expected dimension. This generalizes the case of a single hypersurface, due to Poonen. We use this result to give a probabilistic model for the number of rational points of such a complete intersection. A somewhat surprising corollary is that the number of rational points on a random smooth intersection of two surfaces in projective 3-space is strictly less than the number of points on the projective line.