Remarks on double points of plane curves
نویسندگان
چکیده
Abstract We study the relation between type of a double point plane curve and curvilinear 0-dimensional subschemes at point. An Algorithm related to classical procedure for points via osculating curves is described proved. Eventually we look way create examples rational with given singularities $$A_s$$ A s .
منابع مشابه
Singular Points of Plane Curves
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...
متن کاملInflexion Points on Plane Algebraic Curves
In this thesis we will have a look at algebraic curves in the projective plane over an arbitrary algebraically closed field k. Using the resultant of polynomial rings over k we define intersection multiplicities and prove Bézout’s Theorem for effective divisors. We define singularities and inflexion points and count their number depending on the degree of the curve, using the Hessian of a curve.
متن کاملOn Plane Sextics with Double Singular Points
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.
متن کاملComputing singular points of plane rational curves
We compute the singular points of a plane rational curve, parametrically given, using the implicitization matrix derived from the μ-basis of the curve. It is shown that singularity factors, which are defined and uniquely determined by the elementary divisors of the implicitization matrix, contain all the information about the singular points, such as the parameter values of the singular points ...
متن کاملConstructions of Plane Curves with Many Points
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2022
ISSN: ['0046-5755', '1572-9168']
DOI: https://doi.org/10.1007/s10711-022-00732-4