Complex planar curves homeomorphic to a line have at most four singular points
نویسندگان
چکیده
We show that a complex planar curve homeomorphic to the projective line has at most four singular points. If it exactly then degree five and is unique up equivalence. Nous montrons qu'une courbe plane complexe homéomorphe à la droite au plus quatre points singuliers. S'il en exactement quatre, alors il est quintique, équivalence près.
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 کامل5 Local Parametrization of Space Curves at Singular Points
We propose a symbolic computation algorithm for computing local parametrization of analytic branches and real analytic branches of a curve in n-dimensional space, which is de ned by implicit polynomial equations. The algorithm can be used in space curve tracing near a singular point, as an alternative to symbolic computations based on resolutions of singularities.
متن کاملPlanar Posets Have Dimension at Most Linear in Their Height
We prove that every planar poset P of height h has dimension at most 192h + 96. This improves on previous exponential bounds and is best possible up to a constant factor. We complement this result with a construction of planar posets of height h and dimension at least (4/3)h− 2. (G. Joret) Computer Science Department, Université Libre de Bruxelles, Brussels, Belgium (P. Micek) Theoretical Compu...
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 کاملMost Hyperelliptic Curves Have Big Monodromy
ρf,` : Gal(k̄/k)→ Aut(Jf [`](k̄)) ' GL2g(F`) on the `-torsion points of Jf is as big as possible for almost all primes `, if the following two (sufficient) conditions hold: (1) the endomorphism ring of Jf is Z; (2) for some prime ideal p ⊂ Zk, the fiber over p of the Néron model of Cf is a smooth curve except for a single ordinary double point. These conditions can be translated concretely in ter...
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: Journal de Mathématiques Pures et Appliquées
سال: 2022
ISSN: ['0021-7824', '1776-3371']
DOI: https://doi.org/10.1016/j.matpur.2021.11.003