Local embeddings of lines in singular hypersurfaces

Guangfeng Jiang; Dirk Siersma

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 4, page 1129-1147
  • ISSN: 0373-0956

Abstract

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Lines on hypersurfaces with isolated singularities are classified. New normal forms of simple singularities with respect to lines are obtained. Several invariants are introduced.

How to cite

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Jiang, Guangfeng, and Siersma, Dirk. "Local embeddings of lines in singular hypersurfaces." Annales de l'institut Fourier 49.4 (1999): 1129-1147. <http://eudml.org/doc/75375>.

@article{Jiang1999,
abstract = {Lines on hypersurfaces with isolated singularities are classified. New normal forms of simple singularities with respect to lines are obtained. Several invariants are introduced.},
author = {Jiang, Guangfeng, Siersma, Dirk},
journal = {Annales de l'institut Fourier},
keywords = {embedding; lines on hypersurfaces; isolated singularities; -- singularities; lines embedded in a hypersurface; simple surface singularities},
language = {eng},
number = {4},
pages = {1129-1147},
publisher = {Association des Annales de l'Institut Fourier},
title = {Local embeddings of lines in singular hypersurfaces},
url = {http://eudml.org/doc/75375},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Jiang, Guangfeng
AU - Siersma, Dirk
TI - Local embeddings of lines in singular hypersurfaces
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 4
SP - 1129
EP - 1147
AB - Lines on hypersurfaces with isolated singularities are classified. New normal forms of simple singularities with respect to lines are obtained. Several invariants are introduced.
LA - eng
KW - embedding; lines on hypersurfaces; isolated singularities; -- singularities; lines embedded in a hypersurface; simple surface singularities
UR - http://eudml.org/doc/75375
ER -

References

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  1. [1] V.I. ARNOL'D, Normal forms of functions near degenerate critical points, Weyl groups Ak, Dk, Ek and Lagrange singularities, Funct. Anal. Appl., 6, n° 4 (1972), 254-272. Zbl0278.57011
  2. [2] V.I. ARNOL'D, Classification of 1-modular critical points of functions, Funct. Anal. Appl., 7, n° 3 (1972), 230-231. Zbl0294.57018
  3. [3] V.I. ARNOLD, S.M. GUSEIN-ZADE, A.N. VARCHENKO, Singularities of differentiable Maps, Vol. I, II, Birkhäuser, 1985. Zbl1297.32001
  4. [4] A.H. DURFEE, Fifteen characterizations of rational double points and simple critical points, Ens. Math., 25 (1979), 131-163. Zbl0418.14020MR80m:14003
  5. [5] G. GONZALEZ-SPRINBERG, M. LEJEUNE-JALABERT, Families of smooth curves on surface singularities and wedges, Ann. Polonici Math., LXVII, 2 (1997), 179-190. Zbl0894.14017MR99c:14002
  6. [6] R. GUNNING, Lectures on complex analytic varieties II, Finite analytic mappings, Princeton University Press, 1970. Zbl0213.35904
  7. [7] G. JIANG, Functions with non-isolated singularities on singular spaces, Thesis, Universiteit Utrecht, 1998. 
  8. [8] D. SIERSMA, The singularities of C∞-functions of right codimension smaller or equal than eight, Indag. Math., 35, n° 1 (1973), 31-37. Zbl0249.58004MR51 #11574
  9. [9] D. SIERSMA, Classification and deformation of singularities, Thesis, Amsterdam University, 1974. Zbl0283.57012MR50 #3267
  10. [10] D. SIERSMA, Isolated line singularities, Proc. Symp. in Pure Math., 40, Part 2 (1983), 485-496. Zbl0514.32007MR85d:32017

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