Smoothness of the images of members of a linear system under an endomorphism of the affine plane |
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| Authors: | Pierrette Cassou-Noguès |
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| Institution: | a IMB, Université Bordeaux I, 350, Cours de la Libération, 33405 Talence Cedex, France
b School of Science and Technology, Kwansei Gakuin University, 2-1 Gakuen, Sanda, Hyogo 669-1337, Japan |
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| Abstract: | Let φ=(f,g) be an endomorphism of the affine plane C2 defined by two polynomials f,g∈Cx,y] and let Λ={Cb∣b∈C} be the pencil of lines Cb defined by x=b. We shall consider the smoothness criterion of the image curve φ(Cb). The hypersurface V whose coordinate ring is Cx,f,g] and the normalization  of V will play interesting roles in analyzing the properties of the set φ(Λ)={φ(Cb)∣b∈C}. |
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| Keywords: | Primary 14R10 secondary 14R15 |
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