Enriques surfaces and Jacobian elliptic K3 surfaces
Enriques surfaces and Jacobian elliptic K3 surfaces
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Enriques 曲面和雅可比椭圆 K3 曲面
DOI：
10.1007/s00209-010-0708-3
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发表时间：
2009
影响因子：
0.8
通讯作者：
M. Schütt
中科院分区：
文献类型：
--
作者：
K. Hulek;M. Schütt
本文提出了一种新的Enrique曲面的几何构造方法。它的起点是具有雅可比椭圆纤维的K3曲面，它是由有理椭圆曲面通过二次基变换而来的。用这种方法得到的Enrique曲面的特征是在覆盖的K3曲面上用一条有理曲线作为二等分的椭圆纤维。这种构造在具有特定自同构的Enrique曲面的研究中有应用。它还允许我们回答Beauville关于Enrique曲面的问题，这些Enrique曲面的Brauer群表现出特殊的行为。在即将发表的一篇论文中，我们将研究构造的算术结果。
This paper proposes a new geometric construction of Enriques surfaces. Its starting point are K3 surfaces with Jacobian elliptic fibration which arise from rational elliptic surfaces by a quadratic base change. The Enriques surfaces obtained in this way are characterised by elliptic fibrations with a rational curve as bisection which splits into two sections on the covering K3 surface. The construction has applications to the study of Enriques surfaces with specific automorphisms. It also allows us to answer a question of Beauville about Enriques surfaces whose Brauer groups show an exceptional behaviour. In a forthcoming paper, we will study arithmetic consequences of our construction.