In:
International Mathematics Research Notices, Oxford University Press (OUP), Vol. 2022, No. 6 ( 2022-03-11), p. 4503-4513
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.
Type of Medium:
Online Resource
ISSN:
1073-7928
,
1687-0247
DOI:
10.1093/imrn/rnaa182
Language:
English
Publisher:
Oxford University Press (OUP)
Publication Date:
2022
detail.hit.zdb_id:
1465368-0
SSG:
17,1
Permalink