Smoothness of the images of members of a linear system under an endomorphism of the affine plane

Abstract

a b s t r a c tLet ϕ = (f , g) be an endomorphism of the affine plane C 2 defined by two polynomialsWe shall consider the smoothness criterion of the image curve ϕ(C b ). The hypersurface V whose coordinate ring is C[x, f , g] and the normalization V of V will play interesting roles in analyzing the properties of the set ϕ(Λ) = {ϕ(C b ) | b ∈ C}.