Irreducibility of hypersurfaces

Details Irreducibility of hypersurfaces Irreducibility of hypersurfaces

2007-01-31

arxiv.org/abs/math/0701919v1

Mathematics

Number Theory

21 pages

Scientific paper

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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