Bertini irreducibility theorems over finite fields
Name
Poonen_Bertini irreducibility.pdf
Size
230.58 KB
Format
Adobe PDF
Checksum (MD5)
33dd771220d900a44a23ff3106276d06
Author(s)
Charles, François
Poonen, Bjorn
Charles, Francois
Date Issued
October 2014
Journal
Journal of the American Mathematical Society
Publisher
American Mathematical Society
Citation
Charles, François, and Bjorn Poonen. “Bertini Irreducibility Theorems over Finite Fields.” Journal of the American Mathematical Society 29, no. 1 (October 31, 2014): 81–94. © 2014 American Mathematical Society.
Version
Final published version
Abstract
Given a geometrically irreducible subscheme $ X \subseteq \mathbb{P}^n_{\mathbb{F}_q}$ of dimension at least $ 2$, we prove that the fraction of degree $ d$ hypersurfaces $ H$ such that $ H \cap X$ is geometrically irreducible tends to $ 1$ as $ d \to \infty $. We also prove variants in which $ X$ is over an extension of $ \mathbb{F}_q$, and in which the immersion $ X \to \mathbb{P}^n_{\mathbb{F}_q}$ is replaced by a more general morphism.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1090/S0894-0347-2014-00820-1
