论文标题
在某些极端有理椭圆形表面封面上椭圆纤维的定义领域
Fields of definition of elliptic fibrations on covers of certain extremal rational elliptic surfaces
论文作者
论文摘要
我们在数字$ k $上研究K3表面，这是极端理性椭圆表面的双重覆盖。我们在某些K3表面上提供了所有椭圆形振动的列表，以及一个场扩展的程度，在该范围内定义了每个属均纤维，并允许一个部分。我们表明，通常，后者取决于覆盖物相互作用对属1纤维纤维的作用。
We study K3 surfaces over a number field $k$ which are double covers of extremal rational elliptic surfaces. We provide a list of all elliptic fibrations on certain K3 surfaces together with the degree of a field extension over which each genus one fibration is defined and admits a section. We show that the latter depends, in general, on the action of the cover involution on the fibers of the genus 1 fibration.
