On Plane Curves with Double and Triple Points
نویسندگان
چکیده
منابع مشابه
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We compute the fundamental groups of five maximizing sextics with double singular points only; in four cases, the groups are as expected. The approach used would apply to other sextics as well, given their equations.
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In this paper we investigate some plane curves with many points over Q, finite fields and cyclotomic fields. In a previous paper [4] the first two authors constructed a sequence of absolutely irreducible polynomials Pd(x, y) ∈ Z[x, y] of degree d having low height and many integral solutions to Pd(x, y) = 0. (The definition of these polynomials will be recalled in §4.) Here we construct further...
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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: MATHEMATICA SCANDINAVICA
سال: 2016
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-24184