On blowing up versal discriminants

Piotr Jaworski

Banach Center Publications (1998)

  • Volume: 44, Issue: 1, page 129-140
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Jaworski, Piotr. "On blowing up versal discriminants." Banach Center Publications 44.1 (1998): 129-140. <http://eudml.org/doc/208874>.

@article{Jaworski1998,
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.},
author = {Jaworski, Piotr},
journal = {Banach Center Publications},
keywords = {unfoldings; deformations; analytic triviality; moduli; equisingularity; versal discriminant; versality discriminant; instability locus; contact equivalence; liftable vector fields; blowing up; blowing down},
language = {eng},
number = {1},
pages = {129-140},
title = {On blowing up versal discriminants},
url = {http://eudml.org/doc/208874},
volume = {44},
year = {1998},
}

TY - JOUR
AU - Jaworski, Piotr
TI - On blowing up versal discriminants
JO - Banach Center Publications
PY - 1998
VL - 44
IS - 1
SP - 129
EP - 140
AB - 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.
LA - eng
KW - unfoldings; deformations; analytic triviality; moduli; equisingularity; versal discriminant; versality discriminant; instability locus; contact equivalence; liftable vector fields; blowing up; blowing down
UR - http://eudml.org/doc/208874
ER -

References

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  1. [1] V. I. Arnol ' d, S. M. Guseĭn-Zade and A. N. Varchenko, Singularities of Differentiable Maps, vol. 1, Birkhäuser, Boston, 1985. 
  2. [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. Zbl0675.58008
  3. [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. Zbl0822.32005
  4. [4] J. Damon, A. Galligo, Universal topological stratification for the Pham example, Bull. Soc. Math. France 121 (1993), 153-181. Zbl0784.32029
  5. [5] R. Hartshorne, Algebraic Geometry, Graduate Texts in Math. 52, Springer, New York, 1977. 
  6. [6] P. Jaworski, Decompositions of hypersurface singularities of type J k , 0 , Ann. Polon. Math. 59 (1994), 117-131. Zbl0819.32013
  7. [7] P. Jaworski, On the versal discriminant of the J k , 0 singularities, Ann. Polon. Math. 63 (1996), 89-99. Zbl0848.32028
  8. [8] E. Looijenga, Semi-universal deformation of a simple elliptic hypersurface singularity, I: Unimodularity, Topology 16 (1977), 257-262. Zbl0373.32004
  9. [9] 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. 
  10. [10] 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. Zbl0870.57001
  11. [11] K. Wirthmüller, Universell topologische triviale Deformationen, Ph.D. thesis, University of Regensburg, 1979. 

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