关于算术变量的Bertini正则定理

Journal de l’École polytechnique — Mathématiques Pub Date : 2020-02-25 DOI:10.5802/jep.191

Xiaozong Wang

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引用次数: 1

摘要

让 $\mathcal{X}$ 是一个正则的射影算术变异体，配有一个充足的厄米线束 $\overline{\mathcal{L}}$．我们证明了全局截面的比例 $\sigma$ 有 $\left\lVert \sigma \right\rVert_{\infty}<1$ 的 $\overline{\mathcal{L}}^{\otimes d}$ 谁的除数在纤维上没有奇点 $\mathcal{X}_p$ 除以任意质数 $p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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On the Bertini regularity theorem for arithmetic varieties

Let $\mathcal{X}$ be a regular projective arithmetic variety equipped with an ample hermitian line bundle $\overline{\mathcal{L}}$. We prove that the proportion of global sections $\sigma$ with $\left\lVert \sigma \right\rVert_{\infty}<1$ of $\overline{\mathcal{L}}^{\otimes d}$ whose divisor does not have a singular point on the fiber $\mathcal{X}_p$ over any prime $p

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Journal de l’École polytechnique — Mathématiques

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