论文标题
减少生物表面
Reduction of bielliptic surfaces
论文作者
论文摘要
生物纤维表面（或高纤维表面）是具有数字典型的典型分裂的光滑表面，因此阿尔巴尼斯的形态是椭圆形纤维化。在本文的第一部分中，我们研究了与$ 2 $和$ 3 $不同的特征领域的生物表面的结构，以证明Shafarevich的猜想是具有合理点的Bielliptic表面。此外，我们证明了Shafarevich的猜想通常在没有合理点的情况下对生物界面的表面失败。特别是，本文完成了对Kodaira Dimension最小表面$ 0 $的Shafarevich猜想的研究。 在本文的第二部分中，我们研究了生物外表面的néron模型。当残留特性不等于$ 2 $或$ 3 $时，我们确定了néron模型的潜在存在。
A bielliptic surface (or hyperelliptic surface) is a smooth surface with a numerically trivial canonical divisor such that the Albanese morphism is an elliptic fibration. In the first part of this paper, we study the structure of bielliptic surfaces over a field of characteristic different from $2$ and $3$, in order to prove the Shafarevich conjecture for bielliptic surfaces with rational points. Furthermore, we demonstrate that the Shafarevich conjecture generally fails for bielliptic surfaces without rational points. In particular, this paper completes the study of the Shafarevich conjecture for minimal surfaces of Kodaira dimension $0$. In the second part of this paper, we study a Néron model of a bielliptic surface. We establish the potential existence of a Néron model for a bielliptic surface when the residual characteristic is not equal to $2$ or $3$.
