The Exceptional Locus in the Bertini Irreducibility Theorem for a Morphism
Name
bertini_locus.pdf
Description
Accepted version
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425.51 KB
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Author(s)
Poonen, Bjorn
Slavov, Kaloyan
Date Issued
2020
Journal
International Mathematics Research Notices
Publisher
Oxford University Press (OUP)
Version
Author's final manuscript
Abstract
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 $\phi \colon X \to{\mathbb{P}}^n$ such that $X$ is geometrically irreducible and the nonempty fibers of $\phi $ all have the same dimension, the locus of hyperplanes $H$ such that $\phi ^{-1} H$ is not geometrically irreducible has dimension at most ${\operatorname{codim}}\ \phi (X)+1$. We give an application to monodromy groups above hyperplane sections.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1093/IMRN/RNAA182
