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Irreducibility of hypersurfaces

Arnaud Bodin·Pierre Dèbes·Salah Najib
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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.

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Arnaud Bodin, Pierre Dèbes, Salah Najib. 2007-01-31. Irreducibility of hypersurfaces. https://arxiv.org/abs/math/0701919

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