Geometry of Puiseux expansions

• Autorzy: Maciej Borodzik , Henryk Żołądek
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 14H45: Special curves and curves of low genus
• 14B05: Singularities
• 14H20: Singularities, local rings
• 14H50: Plane and space curves

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2008
• Tom: 93
• Numer: 3
• Strony: 263-280

Daty

wydano

2008

Twórcy

autor

Maciej Borodzik

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

autor

Henryk Żołądek

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/ap93-3-7