论文标题
在弱的lefschetz原理上
On the weak Lefschetz principle in birational geometry
论文作者
论文摘要
这是为AMS的通知而写的一篇说明性文章，我们在其中讨论了Birational几何形状中弱的Lefschetz原理。我们的出发点是所罗门·莱夫策兹（Solomon Lefschetz）的有影响力的作品始于1924年。的确，我们研究了代数拓扑中的lefschetz超平面定理的原始表述，并建立在Birational几何学中的最新发展。在此过程中，本文的主题是以下内容：在几何形状中有许多场景，其中lefschetz超平面定理的类似版本。这些情况有些意外，并且对数学产生了深远的影响。
This is an expository article written for the Notices of the AMS in which we discuss the weak Lefschetz Principle in birational geometry. Our departing point is the influential work of Solomon Lefschetz started in 1924. Indeed, we look at the original formulation of the Lefschetz hyperplane theorem in algebraic topology and build up to recent developments of it in birational geometry. In doing so, the main theme of the article is the following: there are many scenarios in geometry in which analogous versions of the Lefschetz hyperplane theorem hold. These scenarios are somewhat unexpected and have had a profound impact in mathematics.
