On blowing up versal discriminants

Piotr Jaworski

ArticleOriginal scientific text

Title

On blowing up versal discriminants

Authors ¹

Affiliations

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

Abstract

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 for analytic triviality of an unfolding or deformation along the moduli. The goal of this paper is to describe the versal discriminant of

Z_{k, 0}

and

Q_{k, 0}

singularities basing on the fact that the deformations of these singularities may be obtained as blowing ups of certain deformations of

J_{k, 0}

singularities.

V. I. Arnol $'$ d, S. M. Guseĭn-Zade and A. N. Varchenko, Singularities of Differentiable Maps, vol. 1, Birkhäuser, Boston, 1985.
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.
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.
J. Damon, A. Galligo, Universal topological stratification for the Pham example, Bull. Soc. Math. France 121 (1993), 153-181.
R. Hartshorne, Algebraic Geometry, Graduate Texts in Math. 52, Springer, New York, 1977.
P. Jaworski, Decompositions of hypersurface singularities of type $J_{k}, 0$ , Ann. Polon. Math. 59 (1994), 117-131.
P. Jaworski, On the versal discriminant of the $J_{k}, 0$ singularities, Ann. Polon. Math. 63 (1996), 89-99.
E. Looijenga, Semi-universal deformation of a simple elliptic hypersurface singularity, I: Unimodularity, Topology 16 (1977), 257-262.
A. du Plessis, C. T. C. Wall, Topological stability, in: Singularities (Lille, 1991), London Math. Soc. Lecture Note Ser. 201, Cambridge Univ. Press, Cambridge, 1994, 351-362.
A. du Plessis, C. T. C. Wall, The Geometry of Topological Stability, London Math. Soc. Monogr. (N.S.) 9, Oxford Sci. Publ., Oxford Univ. Press, New York, 1995.
K. Wirthmüller, Universell topologische triviale Deformationen, Ph.D. thesis, University of Regensburg, 1979.

Title

On blowing up versal discriminants

Affiliations

Abstract

Bibliography