论文标题
阿贝尔品种的平滑性曲面超过算术环
Smooth hypersurfaces in abelian varieties over arithmetic rings
论文作者
论文摘要
让$ a $是$ \ mathbb {z} $ - 有限生成的集成域$ r $的特征零的ABELIAN方案，至少四个。我们证明，代表$ l $的一组光滑的超曲面$ d $是有限的，表明此类Hypersurfaces的Moduli堆栈只有有限的许多$ r $ $ - 点。我们通过使用水平结构来插值且在该模量堆栈之间的有限性结果来实现这一目标。
Let $A$ be an abelian scheme of dimension at least four over a $\mathbb{Z}$-finitely generated integral domain $R$ of characteristic zero, and let $L$ be an ample line bundle on $A$. We prove that the set of smooth hypersurfaces $D$ in $A$ representing $L$ is finite by showing that the moduli stack of such hypersurfaces has only finitely many $R$-points. We accomplish this by using level structures to interpolate finiteness results between this moduli stack and the stack of canonically polarized varieties.
