Bertini irreducibility theorems over finite fields
Authors:
François Charles and Bjorn Poonen
Journal:
J. Amer. Math. Soc. 29 (2016), 81-94
MSC (2010):
Primary 14J70; Secondary 14N05
DOI:
https://doi.org/10.1090/S0894-0347-2014-00820-1
Published electronically:
October 31, 2014
Erratum:
J. Amer. Math. Soc. 32 (2019), 605-607.
MathSciNet review:
3402695
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Abstract | References | Similar Articles | Additional Information
Abstract: Given a geometrically irreducible subscheme of dimension at least
, we prove that the fraction of degree
hypersurfaces
such that
is geometrically irreducible tends to
as
. We also prove variants in which
is over an extension of
, and in which the immersion
is replaced by a more general morphism.
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Additional Information
François Charles
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307; and CNRS, Laboratoire de Mathématiques d’Orsay,Université Paris-Sud, 91405 Orsay CEDEX, France
Email:
francois.charles@math.u-psud.fr
Bjorn Poonen
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307
Email:
poonen@math.mit.edu
DOI:
https://doi.org/10.1090/S0894-0347-2014-00820-1
Keywords:
Bertini irreducibility theorem,
finite field
Received by editor(s):
November 27, 2013
Received by editor(s) in revised form:
July 4, 2014, July 7, 2014, and September 15, 2014
Published electronically:
October 31, 2014
Additional Notes:
This material is based upon work supported by the National Science Foundation under grant number DMS-1069236. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
Article copyright:
© Copyright 2014
American Mathematical Society