Newton polyhedra of discriminants: a computation
- Evelia García Barroso 1
- Bernard Teissier
-
1
Universidad de La Laguna
info
Verlag: Cambridge University press
ISBN: 978-0-521-68309-8
Datum der Publikation: 2006
Ausgabe: 324
Seiten: 185-210
Art: Buch-Kapitel
Zusammenfassung
We compute the Newton polyhedron in the natural coordinates of thediscriminant of a germ of complex analytic mapping (C3 ×C,0) →(C3 ×C,0) associated by the polar hypersurface construction to thedegeneration of a plane analytic branch with two characteristic pairsto the monomial curve with the same semigroup. The result showsthat the jacobian Newton polyhedron is not in general constant inan equisingular family of complete intersection branches (whereas itis constant in an equisingular family of plane branches). However, inthis case the information that it contains, namely the semigroup, isconstant and only the encoding changes.
Bibliographische Referenzen
- [1] Bourbaki, N.: El ́ements de Math ́ematique. Alg` ebre Chap. III, Hermann (1970).
- [2] Gelfand, I.M.; Kapranov, M.M.; Zelevinsky, A.V.: Discriminants, resul- tants, and multidimensional determinants. Birkha ̈ user, Boston, 1994.
- [3] Garcia Barroso, E.R.; Teissier, B.: Concentration multi- ́echelles de cour- bure dans des fibres de Milnor. Comment. Math. Helv. 74, 398–418 (1999).
- [4] Lˆe, D.T.; Michel, F.; Weber, C.: Sur le comportement des polaires as- soci ́ees aux courbes planes. Compositio Math. 72, 87–113 (1989).
- [5] Merle, M.: Invariants polaires des courbes planes. Invent. Math. 41, 103– 111 (1977).
- [6] Teissier, B.: The hunting of invariants in the geometry of discriminants. In: Proc. Nordic summer school, 1976. Per Holm, editor, Sijthoff and Noordhoff 1978, 565–677.
- [7] Teissier, B.: Appendice in [9].
- [8] Teissier, B.: Multiplicit ́es polaires, sections planes, et conditions de Whit- ney. In: Proc. La Rabida Conference 1981, Springer Lecture Notes in Math., No. 961, 314–489.
- [9] Zariski, O.: Le probl`eme des modules pour les branches planes. Centre de Maths, Ecole Polytechnique, 1975. Republi ́e par Hermann, Paris 1986.