Geometry of Puiseux expansions

Maciej Borodzik, and Henryk Żołądek. "Geometry of Puiseux expansions." Annales Polonici Mathematici 93.3 (2008): 263-280. <http://eudml.org/doc/280394>.

@article{MaciejBorodzik2008,
abstract = {We consider the space Curv of complex affine lines t ↦ (x,y) = (ϕ(t),ψ(t)) with monic polynomials ϕ, ψ of fixed degrees and a map Expan from Curv to a complex affine space Puis with dim Curv = dim Puis, which is defined by initial Puiseux coefficients of the Puiseux expansion of the curve at infinity. We present some unexpected relations between geometrical properties of the curves (ϕ,ψ) and singularities of the map Expan. For example, the curve (ϕ,ψ) has a cuspidal singularity iff it is a critical point of Expan. We calculate the geometric degree of Expan in the cases gcd(degϕ,degψ) ≤ 2 and describe the non-properness set of Expan.},
author = {Maciej Borodzik, Henryk Żołądek},
journal = {Annales Polonici Mathematici},
keywords = {Puiseux expansion; affine algebraic curve},
language = {eng},
number = {3},
pages = {263-280},
title = {Geometry of Puiseux expansions},
url = {http://eudml.org/doc/280394},
volume = {93},
year = {2008},
}

TY - JOUR
AU - Maciej Borodzik
AU - Henryk Żołądek
TI - Geometry of Puiseux expansions
JO - Annales Polonici Mathematici
PY - 2008
VL - 93
IS - 3
SP - 263
EP - 280
AB - We consider the space Curv of complex affine lines t ↦ (x,y) = (ϕ(t),ψ(t)) with monic polynomials ϕ, ψ of fixed degrees and a map Expan from Curv to a complex affine space Puis with dim Curv = dim Puis, which is defined by initial Puiseux coefficients of the Puiseux expansion of the curve at infinity. We present some unexpected relations between geometrical properties of the curves (ϕ,ψ) and singularities of the map Expan. For example, the curve (ϕ,ψ) has a cuspidal singularity iff it is a critical point of Expan. We calculate the geometric degree of Expan in the cases gcd(degϕ,degψ) ≤ 2 and describe the non-properness set of Expan.
LA - eng
KW - Puiseux expansion; affine algebraic curve
UR - http://eudml.org/doc/280394
ER -