Base points of polar curves

Eduardo Casas-Alvero

Annales de l'institut Fourier (1991)

  • Volume: 41, Issue: 1, page 1-10
  • ISSN: 0373-0956

Abstract

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The base points of the system of polar curves of an irreducible algebroid plane curve with general moduli are determined. As consequences a lower bound for the Tjurina number and many continuous analytic invariants of the curve are found.

How to cite

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Casas-Alvero, Eduardo. "Base points of polar curves." Annales de l'institut Fourier 41.1 (1991): 1-10. <http://eudml.org/doc/74914>.

@article{Casas1991,
abstract = {The base points of the system of polar curves of an irreducible algebroid plane curve with general moduli are determined. As consequences a lower bound for the Tjurina number and many continuous analytic invariants of the curve are found.},
author = {Casas-Alvero, Eduardo},
journal = {Annales de l'institut Fourier},
keywords = {singularity of plane; base points of the system of polar curves; algebroid plane curve; Tjurina number},
language = {eng},
number = {1},
pages = {1-10},
publisher = {Association des Annales de l'Institut Fourier},
title = {Base points of polar curves},
url = {http://eudml.org/doc/74914},
volume = {41},
year = {1991},
}

TY - JOUR
AU - Casas-Alvero, Eduardo
TI - Base points of polar curves
JO - Annales de l'institut Fourier
PY - 1991
PB - Association des Annales de l'Institut Fourier
VL - 41
IS - 1
SP - 1
EP - 10
AB - The base points of the system of polar curves of an irreducible algebroid plane curve with general moduli are determined. As consequences a lower bound for the Tjurina number and many continuous analytic invariants of the curve are found.
LA - eng
KW - singularity of plane; base points of the system of polar curves; algebroid plane curve; Tjurina number
UR - http://eudml.org/doc/74914
ER -

References

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  1. [1] E. CASAS-ALVERO, Moduli of algebroid plane curves, Algebraic Geometry, La Rábida 1981, Lecture Notes in Math 961, Springer Verlag, 1982, 32-83. Zbl0515.14019MR85g:14028
  2. [2] E. CASAS-ALVERO, Infinitely near singularities and singularities of polar curves, Math. Ann., 287 (1990), 429-454. Zbl0675.14009MR91h:14002
  3. [3] F. ENRIQUES, O. CHISINI, Teoria Geometrica delle Equazioni e delle Funzioni Algebriche, N. Zanichelli, Bologna, 1915. JFM45.1356.02
  4. [4] J. G. SEMPLE, G.T. KNEEBONE, Algebraic Curves, Oxford University Press, London, 1959. Zbl0105.34301MR23 #A2111
  5. [5] O. ZARISKI, Characterization of plane curves whose module of differentials has maximal torsion, Proc. Nat. Acad. of Science, U.S.A., 56,3 (1966), 781-786. Zbl0144.20201MR34 #2576
  6. [6] O. ZARISKI, Le problème des modules pour les branches planes, Centre de Math., École Polytechnique, Paris, 1973. Zbl0317.14004MR54 #2662

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