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Communications in Algebra
Article
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arXiv.org e-Print Archive
Preprint . 2007
Data sources: arXiv.org e-Print Archive
Communications in Algebra
Article . 2009 . Peer-reviewed
Data sources: Crossref
https://dx.doi.org/10.48550/ar...
Article . 2007
License: arXiv Non-Exclusive Distribution
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Communications in Algebra
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Irreducibility of Hypersurfaces

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 04 Jun 2009Embargo end date: 01 Jan 2007Publisher:Informa UK LimitedJournal:Communications in Algebra, volume 37, pages 1,884-1,900 (issn: 0092-7872, eissn: 1532-4125, Copyright policy )
Authors: Arnaud Bodin; Pierre Dèbes; Salah Najib;

doi: 10.1080/00927870802116562 , 10.48550/arxiv.math/0701919

arXiv: http://arxiv.org/abs/math/0701919

Irreducibility of Hypersurfaces

Abstract

Given a polynomial P in several variables over an algebraically closed field, we show that except in some special cases that we fully describe, if one coefficient is allowed to vary, then the polynomial is irreducible for all but at most deg(P)^2-1 values of the coefficient. We more generally handle the situation where several specified coefficients vary.

21 pages

Related Organizations
Keywords

Mathematics - Algebraic Geometry, Mathematics - Number Theory, 11C08, FOS: Mathematics, 12E05; 11C08, 12E05, Number Theory (math.NT), Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Algebraic Geometry (math.AG)

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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 10
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
10
Average
Top 10%
Average
Green
bronze