On vanishing inflection points of plane curves

Mauricio Garay[1]

  • [1] Université Paris VII, UFR de Mathématiques, Case 7012, 2 place Jussieu, 75251 Paris Cedex 05 (France)

Annales de l’institut Fourier (2002)

  • Volume: 52, Issue: 3, page 849-880
  • ISSN: 0373-0956

Abstract

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We study the local behaviour of inflection points of families of plane curves in the projective plane. We develop normal forms and versal deformation concepts for holomorphic function germs f : ( ℂ 2 , 0 ) ⟶ ( ℂ , 0 ) which take into account the inflection points of the fibres of f . We give a classification of such function- germs which is a projective analog of Arnold’s A,D,E classification. We compute the versal deformation with respect to inflections of Morse function-germs.

How to cite

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Garay, Mauricio. "On vanishing inflection points of plane curves." Annales de l’institut Fourier 52.3 (2002): 849-880. <http://eudml.org/doc/115997>.

@article{Garay2002,
abstract = {We study the local behaviour of inflection points of families of plane curves in the projective plane. We develop normal forms and versal deformation concepts for holomorphic function germs $f : (\{\mathbb \{C\}\}^2,0)\longrightarrow (\{\mathbb \{C\}\},0)$ which take into account the inflection points of the fibres of $f$. We give a classification of such function- germs which is a projective analog of Arnold’s A,D,E classification. We compute the versal deformation with respect to inflections of Morse function-germs.},
affiliation = {Université Paris VII, UFR de Mathématiques, Case 7012, 2 place Jussieu, 75251 Paris Cedex 05 (France)},
author = {Garay, Mauricio},
journal = {Annales de l’institut Fourier},
keywords = {Plücker formulas; normal forms; inflection points; bifurcation diagrams; projective geometry},
language = {eng},
number = {3},
pages = {849-880},
publisher = {Association des Annales de l'Institut Fourier},
title = {On vanishing inflection points of plane curves},
url = {http://eudml.org/doc/115997},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Garay, Mauricio
TI - On vanishing inflection points of plane curves
JO - Annales de l’institut Fourier
PY - 2002
PB - Association des Annales de l'Institut Fourier
VL - 52
IS - 3
SP - 849
EP - 880
AB - We study the local behaviour of inflection points of families of plane curves in the projective plane. We develop normal forms and versal deformation concepts for holomorphic function germs $f : ({\mathbb {C}}^2,0)\longrightarrow ({\mathbb {C}},0)$ which take into account the inflection points of the fibres of $f$. We give a classification of such function- germs which is a projective analog of Arnold’s A,D,E classification. We compute the versal deformation with respect to inflections of Morse function-germs.
LA - eng
KW - Plücker formulas; normal forms; inflection points; bifurcation diagrams; projective geometry
UR - http://eudml.org/doc/115997
ER -

References

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