On vanishing inflection points of plane curves
نویسندگان
چکیده
منابع مشابه
Inflection Points on Real Plane Curves Having Many Pseudo-Lines
A pseudo-line of a real plane curve C is a global real branch of C(R) that is not homologically trivial in P(R). A geometrically integral real plane curve C of degree d has at most d− 2 pseudo-lines, provided that C is not a real projective line. Let C be a real plane curve of degree d having exactly d − 2 pseudo-lines. Suppose that the genus of the normalization of C is equal to d− 2. We show ...
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C be the normalization of Γ . Let g = (d− 1)(d− 2) 2 − δ; the genus of C. We identify smooth points of Γ with the corresponding points on C. In particular, if P is a smooth point on Γ then the Weierstrass gap sequence at P is considered with respect to C. A smooth point P ∈ Γ is called an (e − 2)-inflection point if i(Γ, T ;P ) = e ≥ 3 where T is the tangent line to Γ at P (cf. Brieskorn–Knörre...
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ly isomorphic to (C×)r−1 × (C), and hence also to (S1)r−1 × (R), where r = |J | is the number of branches and k = δ(C)− r+1 = 1 2 (μ(C) + 1 − r). The construction of the Jacobian variety J(C̃) of the non-singular curve C̃ in the large is standard in algebraic geometry. There is also a notion of Jacobian of a singular curve C , defined e.g. in [85], which, like the other, is an abelian group. Ther...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2002
ISSN: 0373-0956
DOI: 10.5802/aif.1904