A factorization theorem for the polar of a curve with two branches

Félix Delgado de la Mata

Compositio Mathematica (1994)

  • Volume: 92, Issue: 3, page 327-375
  • ISSN: 0010-437X

How to cite

top

Delgado de la Mata, Félix. "A factorization theorem for the polar of a curve with two branches." Compositio Mathematica 92.3 (1994): 327-375. <http://eudml.org/doc/90310>.

@article{DelgadodelaMata1994,
author = {Delgado de la Mata, Félix},
journal = {Compositio Mathematica},
keywords = {multiplicity of intersection; factorization theorem for the polar of an algebroid curve},
language = {eng},
number = {3},
pages = {327-375},
publisher = {Kluwer Academic Publishers},
title = {A factorization theorem for the polar of a curve with two branches},
url = {http://eudml.org/doc/90310},
volume = {92},
year = {1994},
}

TY - JOUR
AU - Delgado de la Mata, Félix
TI - A factorization theorem for the polar of a curve with two branches
JO - Compositio Mathematica
PY - 1994
PB - Kluwer Academic Publishers
VL - 92
IS - 3
SP - 327
EP - 375
LA - eng
KW - multiplicity of intersection; factorization theorem for the polar of an algebroid curve
UR - http://eudml.org/doc/90310
ER -

References

top
  1. [A] S.S. Abhyankar, "Expansion technics in Algebraic Geometry," Tata Institute of Fundamental Research, Bombay, 1977. Zbl0818.14001MR542446
  2. [An] G. Angermüller, Die wertehalbgrupp einer ebenen irreduziblen algebroiden kurve, Math. Zeitschrift153 (1977), 267-282. Zbl0331.14015MR447227
  3. [Ap] R. Apery, Sur les branches superlineaires des courbes algébriques, C.R. Acad. Sci. Paris222 (1945), 1198-1200. Zbl0061.35404MR17942
  4. [Az] A. Azevedo, The jacobian ideal of a plane algebroid curve, Thesis, Purdue University (1967). 
  5. [B] V. Bayer, Semigroups of two irreducible algebroid curves, Manuscripta Math.49 (1985), 207-241. Zbl0581.14021MR777126
  6. [B-K] E. Brieskorn and H. Knörrer, Plane Algebraic curves, Birkhäuser Verlag, Basel, 1986. Zbl0588.14019MR886476
  7. [C] A. Campillo, Algebroid curves in positive characteristic, Lecture Notes in Math. 813, Springer Verlag, Heidelberg, Berlin, New York. Zbl0451.14010
  8. [Ca] E. Casas, Infinitely near imposed singularities and singularities of polar curves, Math. Annalen287 (1990), 429-454. Zbl0675.14009MR1060685
  9. [D] F. Delgado, The semigroup of values of a curve singularity with several branches, Manuscripta Math.59 (1987), 347-374. Zbl0611.14025MR909850
  10. [D2] F. Delgado, Arithmetical factorizations of critical point sets for some map germs of C2, Preprint, Valladolid University (1991/92). MR1295072
  11. [E] R. Ephraim, Special polars and curves with one place at infinity, Proceedings of Simposia in Pure Math.40 (1983), 353-359. Zbl0537.14020MR713074
  12. [Ga] A. Garcia, The semigroup of a singular point of a curve with two equisingular branches, Manuscripta Math.44 (1983), 51-58. Zbl0529.14014MR709844
  13. [G] A. Granja, Apery basis and polar invariants of plane curve singularities, Pacific Journal of Math.140 (1989), 85-96. Zbl0728.14029MR1019068
  14. [H] H. Hironaka, Introduction to the theory of infinitely near singular points, Memorias del Instituto Jorge Juan, Madrid, 1974. Zbl0366.32007MR399505
  15. [He] J. Herzog, Generators and relations of abelian semigroups and semigroup rings, Manuscripta Math.3 (1970), 175-193. Zbl0211.33801MR269762
  16. [K-L] T.-C. Kuo and Y.-C. Lu, On analytic function germs of two variables, Topology16 (1983), 299-310. Zbl0378.32001MR460711
  17. [LMW] D.T. Lê, F. Michel and C. Weber, Courbes polaires et topologie des courbes plaines, Ann. Scient. ec. Norm. Sup4e Serie, t.24 (1991), 141-169. Zbl0748.32018MR1097689
  18. [LMW2] D.T. Lê, F. Michel and C. Weber, Sur le comportement des polaires associes aux germs de courbes planes, Compositio Math.72 (1989), 87-113. Zbl0705.32021MR1026330
  19. [M] M. Merle, Invariants polaires des courbes planes, Inventiones Math.41 (1977), 103-111. Zbl0371.14003MR460336
  20. [P] H. Pinkham, Courbes planes ayant une seule place à l'infini, Publications du Centre de Mathematiques de l'Ecole Polytechnique (1977-78), Palaiseau. 
  21. [P1] A. Ploski, Remarque sus la multiplicité d'intersection des branches planes, Bull. of the Polish Academy of Sciences33 (1985), 601-605. Zbl0606.32001MR849408
  22. [SZ] J. Steenbrink, S. Zucker, Polar curves, resolution of singularities and the filtered Mixed Hodge Structure on the vanishing cohomology, in "Singularities. Representation of Algebras and Vector Bundles," Lecture Notes in Math. 1273, Springer-Verlag, Heidelberg, Berlin, New York, 1989, pp. 178-202. Zbl0644.14004MR915175
  23. [T] B. Teissier, Varietés polaires I. Invariants polaires des singularités d'hypersurfaces, Inventiones Math. 40, 267-292. Zbl0446.32002MR470246
  24. [Z] O. Zariski, Studies in Equisingularity I, II and III, Amer. J. of Math.; I, 87 (1965), 507-536; II, 87 (1965), 972-1006; III, 90 (1968), 961-1023. Zbl0189.21405
  25. [Z2] O. Zariski, General theory of saturation and of saturated rings. II Saturated local rings of dimension 1, Amer. J. of Math.93 (1971), 872-964. Zbl0228.13007MR299607

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.