PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1997 | 67 | 2 | 179-190
Tytuł artykułu

Families of smooth curves on surface singularities and wedges

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Following the study of the arc structure of singularities, initiated by J. Nash, we give criteria for the existence of smooth curves on a surface singularity (S,O) and of smooth branches of its generic hypersurface section. The main applications are the following: the existence of a natural partition of the set of smooth curves on (S,O) into families, a description of each of them by means of chains of infinitely near points and their associated maximal cycle and the existence of smooth curves on any sandwiched surface singularity. A wedge centered at a smooth curve on (S,O) is essentially a one-parameter deformation of the parametrization of the curve. We show that there is no wedge centered at smooth curves of two different families.
Słowa kluczowe
Rocznik
Tom
67
Numer
2
Strony
179-190
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-10-17
Twórcy
  • Université de Grenoble I, Institut Fourier, UMR 5582 du CNRS et de l'UJF, UFR de Mathématiques, B.P. 74, 38402 St. Martin d'Hères Cedex (France)
  • Université de Grenoble I, Institut Fourier, UMR 5582 du CNRS et de l'UJF, UFR de Mathématiques, B.P. 74, 38402 St. Martin d'Hères Cedex (France)
Bibliografia
  • [A] M. Artin, On isolated rational singularities of surfaces, Amer. J. Math. 88 (1966), 129-136
  • [E] D. Eisenbud, Open problems in computational algebraic geometry, in: Computational Algebraic Geometry and Commutative Algebra, D. Eisenbud and L. Robbiano (eds.), Cambridge Univ. Press, 1993, 49-70
  • [G-S] G. Gonzalez-Sprinberg, Cycle maximal et invariant d'Euler local des singularités isolées de surface, Topology 21 (1982), 401-408
  • [G/L1] G. Gonzalez-Sprinberg et M. Lejeune-Jalabert, Courbes lisses sur les singularités de surface, C. R. Acad. Sci. Paris Sér. I Math. 318 (1994), 653-656
  • [G/L2] G. Gonzalez-Sprinberg et M. Lejeune-Jalabert, Sur l'espace des courbes tracées sur une singularité, in: Algebraic Geometry and Singularities, A. Campillo and L. Narváez (eds.), Progr. Math. 134, Birkhäuser, 1996, 9-32
  • [L] J. Lipman, Desingularization of two-dimensional schemes, Ann. of Math. 107 (1978), 151-207
  • [L-J] M. Lejeune-Jalabert, Arcs analytiques et résolution minimale des singularités des surfaces quasi-homogènes, in: Lecture Notes in Math. 777, Springer, 1980, 303-336
  • [L/T] M. Lejeune-Jalabert et B. Teissier, Contributions à l'étude des singularités du point de vue du polygone de Newton, Thèse, Université Paris 7, 1973
  • [N] J. Nash, Arc structure of singularities, preprint, 1968; Duke Math. J. 81 (1995), 31-38
  • [S] M. Spivakovsky, Sandwiched singularities and desingularization of surfaces by normalized Nash transformations, Ann. of Math. 131 (1990), 411-491
  • [W] R. Walker, Reduction of the singularities of an algebraic surface, Ann. of Math. 36 (1935), 336-36
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv67z2p179bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.