We consider the parameterization f=(f0:f1:f2)of a plane rational curve C of degree n, and we study the singularities of C via such parameterization. We use the projection from the rational normal curve Cn⊂Pn to C and its interplay with the secant varieties to Cn. In particular, we define via f certain 0-dimensional schemes Xk⊂Pk, 2≤k≤(n−1), which encode all information on the singularities of multiplicity ≥k of C (e.g. using X2 we can give a criterion to determine whether C is a cuspidal curve or has only ordinary singularities). We give a series of algorithms which allow one to obtain information about the singularities from such schemes.

Singularities of plane rational curves via projections

Gimigliano, Alessandro;Idà, Monica
2018

Abstract

We consider the parameterization f=(f0:f1:f2)of a plane rational curve C of degree n, and we study the singularities of C via such parameterization. We use the projection from the rational normal curve Cn⊂Pn to C and its interplay with the secant varieties to Cn. In particular, we define via f certain 0-dimensional schemes Xk⊂Pk, 2≤k≤(n−1), which encode all information on the singularities of multiplicity ≥k of C (e.g. using X2 we can give a criterion to determine whether C is a cuspidal curve or has only ordinary singularities). We give a series of algorithms which allow one to obtain information about the singularities from such schemes.
2018
Gimigliano, Alessandro; Bernardi, Alessandra; Idà, Monica
File in questo prodotto:
File Dimensione Formato  
1-s2.0-S0747717117300524-main.pdf

accesso aperto

Tipo: Postprint
Licenza: Licenza per Accesso Aperto. Creative Commons Attribuzione - Non commerciale - Non opere derivate (CCBYNCND)
Dimensione 697.96 kB
Formato Adobe PDF
697.96 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/592019
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 9
  • ???jsp.display-item.citation.isi??? 8
social impact