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.
On détermine les points-base du système des courbes polaires d’une courbe algébroïde plane irréductible à modules généraux. On en tire une borne inférieure pour le nombre de Tjurina et plusieurs invariants analytiques continus de la courbe.
@article{AIF_1991__41_1_1_0, author = {Casas-Alvero, Eduardo}, title = {Base points of polar curves}, journal = {Annales de l'Institut Fourier}, pages = {1--10}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {41}, number = {1}, year = {1991}, doi = {10.5802/aif.1245}, mrnumber = {92f:14023}, zbl = {0707.14024}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1245/} }
Casas-Alvero, Eduardo. Base points of polar curves. Annales de l'Institut Fourier, Volume 41 (1991) no. 1, pp. 1-10. doi : 10.5802/aif.1245. http://www.numdam.org/articles/10.5802/aif.1245/
[1] Moduli of algebroid plane curves, Algebraic Geometry, La Rábida 1981, Lecture Notes in Math 961, Springer Verlag, 1982, 32-83. | MR | Zbl
,[2] Infinitely near singularities and singularities of polar curves, Math. Ann., 287 (1990), 429-454. | MR | Zbl
,[3] Teoria Geometrica delle Equazioni e delle Funzioni Algebriche, N. Zanichelli, Bologna, 1915.
, ,[4] Algebraic Curves, Oxford University Press, London, 1959. | MR | Zbl
, ,[5] Characterization of plane curves whose module of differentials has maximal torsion, Proc. Nat. Acad. of Science, U.S.A., 56,3 (1966), 781-786. | MR | Zbl
,[6] Le problème des modules pour les branches planes, Centre de Math., École Polytechnique, Paris, 1973. | MR | Zbl
,Cited by Sources: