论文标题
贝蒂尼和诺斯科特
Bertini and Northcott
论文作者
论文摘要
我们证明了一种新的Bertini-Type定理，并明确控制了构建曲线的属，程度，高度和定义场。结果，我们提供了一种一般策略，以降低一定的高度和对雅各布品种在适当扩展为$ k $的情况下定义的jacobian品种的一定身高和排名估算。
We prove a new Bertini-type Theorem with explicit control of the genus, degree, height, and the field of definition of the constructed curve. As a consequence we provide a general strategy to reduce certain height and rank estimates on abelian varieties over a number field $K$ to the case of jacobian varieties defined over a suitable extension of $K$.
