The Brauer-Manin Obstruction and III[2]
The Brauer-Manin Obstruction and III[2]
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布劳尔-马宁障碍和 III[2]
DOI：
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发表时间：
2007
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影响因子：
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通讯作者：
A. Logan
中科院分区：
文献类型：
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作者：
M. Bright;Nils Bruin;E. V. Flynn;A. Logan
本文讨论了4次del Pezzo曲面上的Brauer-Manin障碍。我们概述了一个详细的算法计算的障碍，并提供相关的程序在岩浆。这是说明了一个例子的计算与一个不可约的三次因子的定义铅笔的二次曲面的奇异轨迹（与以前的例子相比，在最坏的二次不可约因子）。我们利用与Tate-Shafarevich群的关系给出Sha[2]的新类型的例子，对于形式为y^2 = f（x）的亏格为2的曲线族，其中f（x）是包含不可约三次因子的五次曲线。
We discuss the Brauer-Manin obstruction on del Pezzo surfaces of degree 4. We outline a detailed algorithm for computing the obstruction and provide associated programs in magma. This is illustrated with the computation of an example with an irreducible cubic factor in the singular locus of the defining pencil of quadrics (in contrast to previous examples, which had at worst quadratic irreducible factors). We exploit the relationship with the Tate-Shafarevich group to give new types of examples of Sha[2], for families of curves of genus 2 of the form y^2 = f(x), where f(x) is a quintic containing an irreducible cubic factor.