论文标题
Bertini不可约性定理中的特殊基因座
The exceptional locus in the Bertini irreducibility theorem for a morphism
论文作者
论文摘要
我们基于有限场上的随机超平面切片，在任意领域引入了一种新的方法，以在任意领域的贝蒂尼不可约性定理。扩展了Benoist的结果，我们证明，对于形态性$ ϕ \ colon x \ to \ mathbb {p}^n $ $ \ operatatorName {codim} ϕ（x）+1 $。我们向超平面切片以上的单型组提供了应用。
We introduce a novel approach to Bertini irreducibility theorems over an arbitrary field, based on random hyperplane slicing over a finite field. Extending a result of Benoist, we prove that for a morphism $ϕ\colon X \to \mathbb{P}^n$ such that $X$ is geometrically irreducible and the nonempty fibers of $ϕ$ all have the same dimension, the locus of hyperplanes $H$ such that $ϕ^{-1} H$ is not geometrically irreducible has dimension at most $\operatorname{codim} ϕ(X)+1$. We give an application to monodromy groups above hyperplane sections.
