源于同源椭圆曲线的Inose曲面的Mordell-Weil格

Mordell-Weil lattice of Inose's Elliptic $K3$ surface arising from the product of 3-isogenous elliptic curves

From the product of two elliptic curves, Shioda and Inose constructed an elliptic $K3$ surface having two $\mathrm{II}^*$ fibers. Its Mordell-Weil lattice structure depends on the morphisms between the two elliptic curves. In this paper, we give a method of writing down generators of the Mordell-Weil lattice of such elliptic surfaces when two elliptic curves are $3$-isogenous. In particular, we obtain a basis of the Mordell-Weil lattice for the singular $K3$ surfaces $X_{[3,3,3]}$, $X_{[3,2,3]}$ and $X_{[3,0,3]}$.

Inose's construction and elliptic K3 surfaces with Mordell-Weil rank 15 revisited

We describe two constructions of elliptic K3 surfaces starting from the Kummer surface of the Jacobian of a genus 2 curve. These parallel the base-change constructions of Kuwata for the Kummer surface of a product of two elliptic curves. One of these also involves the analogue of an Inose fibration. We use these methods to provide explicit examples of elliptic K3 surfaces over the rationals of geometric Mordell-Weil rank 15.

Elliptic K3 surfaces admitting a Shioda-Inose structure

We study elliptic K3 surfaces with Mordell Weil rank 0, and which has a 2-torsion section $σ$ such that the translation by $σ$ gives a Shioda-Inose structure.

雅可比曲面的同源分量

Isogenous components of Jacobian surfaces

该研究针对亏格2曲线的雅可比簇，在不同自同构群、可约性参数及同源次数下，计数并分析椭圆分量的同源性，确定相关曲面，指出正特征下的结果可应用于密码学。

Elliptic K3 surfaces associated with the product of two elliptic curves: Mordell-Weil lattices and their fields of definition

To a pair of elliptic curves, one can naturally attach two K3 surfaces: the Kummer surface of their product and a double cover of it, called the Inose surface. They have prominently featured in many interesting constructions in algebraic geometry and number theory. There are several more associated elliptic K3 surfaces, obtained through base change of the Inose surface; these have been previously studied by Kuwata. We give an explicit description of the geometric Mordell-Weil groups of each of these elliptic surfaces in the generic case (when the elliptic curves are non-isogenous). In the non-…

极值椭圆K3曲面的分类及开K3曲面的基本群

Classification of extremal elliptic K3 surfaces and fundamental groups of open K3 surfaces

给出了极值椭圆K3曲面的完整列表。总共有325个。前112个与Miranda-Escherson的半稳定列表相吻合。这些数据包括超越晶格，它确定唯一的K3表面的结果Shioda和Inose，奇异纤维类型和Mordell Weil群。作为应用，我们给出了K3曲面上光滑有理曲线的ADE-构形的补的拓扑基本群为平凡的一个充分条件.