Construction of a del Pezzo surface with maximal Galois action on its Picard group
Construction of a del Pezzo surface with maximal Galois action on its Picard group
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皮卡群上具有最大伽罗瓦作用的德尔佩佐曲面的构造
DOI：
10.1016/0022-4049(94)90037-x
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
R. Erné
中科院分区：
文献类型：
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作者：
R. Erné
域K上的d次del Pezzo曲面是K上的光滑射影曲面X，使得存在一个有限域扩张，在该有限域扩张上X同构于在“一般”位置上在9-d有理点上爆破的P2.本文给出了Q上具有极大Galois作用的2次del Pezzo曲面在Pic（X Q <$）上的一个具体构造.我们遵循Ekedahl在[3]中给出的方法，作为证明该文章主要结果的技术的应用，他在Q（三次曲面）上构造了一个具有此性质的3度del Pezzo曲面。
A del Pezzo surface of degree d over a field K is a smooth projective surface X over K such that there exists a finite field extension over which X is isomorphic to P 2 blown up in 9—d rational points in “general” position. In this paper we give a detailed construction of a del Pezzo surface of degree 2 over Q having maximal Galois action on Pic (X Q ̄). We follow the method given by Ekedahl in [3] where, as an application of techniques used to prove the main result of that article, he constructs a del Pezzo surface of degree 3 over Q (a cubic surface) having this property.