On the versal discriminant of $J_{k,0}$ singularities

• Autorzy: Piotr Jaworski
• Języki publikacji: EN

Abstrakty

EN

It is well known that the versal deformations of nonsimple singularities depend on moduli. The first step in deeper understanding of this phenomenon is to determine the versal discriminant, which roughly speaking is an obstacle to analytic triviality of an unfolding or deformation along the moduli. The versal discriminant of the Pham singularity ($J_{3,0}$ in Arnold's classification) was thoroughly investigated by J. Damon and A. Galligo [2], [3], [4]. The goal of this paper is to continue their work and to describe the versal discriminant of a general $J_{k,0}$ singularity.

Słowa kluczowe

EN

versal deformation; versal unfolding; moduli; liftable vector fields; local algebra; topological triviality

Kategorie tematyczne

• 14B07: Deformations of singularities
• 32S30: Deformations of singularities; vanishing cycles

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996
• Tom: 63
• Numer: 1
• Strony: 89-99

Daty

wydano

1996

otrzymano

1995-03-03

Twórcy

autor

Piotr Jaworski

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Bibliografia

• [1] V. I. Arnold, S. M. Gusein-Zade and A. N. Varchenko, Singularities of Differentiable Maps, Vol. 1, Birkhäuser, 1985.
• [2] J. Damon, On the Pham example and the universal topological stratification of singularities, in: Singularities, Banach Center Publ. 20, PWN-Polish Scientific Publishers, Warszawa, 1988, 161-167.
• [3] J. Damon, A-equivalence and the equivalence of sections of images and discriminants, in: Singularity Theory and its Applications, Part 1 (Coventry 1988/1989), Lecture Notes in Math. 1492, Springer, Berlin, 1991, 93-121.
• [4] J. Damon and A. Galligo, Universal topological stratification for the Pham example, Bull. Soc. Math. France 121 (1993), 153-181.
• [5] R. Hartshorne, Algebraic Geometry, Springer, Berlin, 1977.
• [6] P. Jaworski, Decompositions of hypersurface singularities of type $J_{k,0}$, Ann. Polon. Math. 59 (1994), 117-131.