Singular plane curves with infinitely many Galois points
نویسندگان
چکیده
منابع مشابه
Affine Curves with Infinitely Many Integral Points
Let C ⊂ An be an irreducible affine curve of (geometric) genus 0 defined by a finite family of polynomials having integer coefficients. In this note we give a necessary and sufficient condition for C to possess infinitely many integer points, correcting a statement of J. H. Silverman (Theoret. Comput. Sci., 2000). Let C be an irreducible affine curve of (geometric) genus 0 in the affine space A...
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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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0. In the course of another investigation we came across a sequence of polynomials Pd ∈ Z[x, y], such that Pd is absolutely irreducible, of degree d, has low height and at least d + 2d + 3 integral solutions to Pd(x, y) = 0. We know of no other family of polynomials of increasing degree with as many integral (or even rational) solutions in terms of their degree, except of course those with infi...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2010
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2009.09.025