Jet schemes of complex plane branches and equisingularity

Hussein Mourtada[1]

  • [1] Université de Versailles Saint-Quentin Laboratoire de Mathématiques de Versailles 45 avenue des États-Unis 78035 Versailles CEDEX (France)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 6, page 2313-2336
  • ISSN: 0373-0956

Abstract

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For m ∈ ℕ , we determine the irreducible components of the m - th Jet Scheme of a complex branch C and we give formulas for their number N ( m ) and for their codimensions, in terms of m and the generators of the semigroup of C . This structure of the Jet Schemes determines and is determined by the topological type of C .

How to cite

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Mourtada, Hussein. "Jet schemes of complex plane branches and equisingularity." Annales de l’institut Fourier 61.6 (2011): 2313-2336. <http://eudml.org/doc/219717>.

@article{Mourtada2011,
abstract = {For $m \in \mathbb\{N\}$, we determine the irreducible components of the $m-$th Jet Scheme of a complex branch $C$ and we give formulas for their number $N(m)$ and for their codimensions, in terms of $m$ and the generators of the semigroup of $C$. This structure of the Jet Schemes determines and is determined by the topological type of $C$.},
affiliation = {Université de Versailles Saint-Quentin Laboratoire de Mathématiques de Versailles 45 avenue des États-Unis 78035 Versailles CEDEX (France)},
author = {Mourtada, Hussein},
journal = {Annales de l’institut Fourier},
keywords = {Jet schemes; singularities of plane curves; jet schemes},
language = {eng},
number = {6},
pages = {2313-2336},
publisher = {Association des Annales de l’institut Fourier},
title = {Jet schemes of complex plane branches and equisingularity},
url = {http://eudml.org/doc/219717},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Mourtada, Hussein
TI - Jet schemes of complex plane branches and equisingularity
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 6
SP - 2313
EP - 2336
AB - For $m \in \mathbb{N}$, we determine the irreducible components of the $m-$th Jet Scheme of a complex branch $C$ and we give formulas for their number $N(m)$ and for their codimensions, in terms of $m$ and the generators of the semigroup of $C$. This structure of the Jet Schemes determines and is determined by the topological type of $C$.
LA - eng
KW - Jet schemes; singularities of plane curves; jet schemes
UR - http://eudml.org/doc/219717
ER -

References

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  9. Mircea Mustaţă, Jet schemes of locally complete intersection canonical singularities, Invent. Math. 145 (2001), 397-424 Zbl1091.14004MR1856396
  10. John F. Nash, Arc structure of singularities, Duke Math. J. 81 (1995), 31-38 Zbl0880.14010MR1381967
  11. Mark Spivakovsky, Valuations in function fields of surfaces, Amer. J. Math. 112 (1990), 107-156 Zbl0716.13003MR1037606
  12. Paul Vojta, Jets via Hasse-Schmidt derivations, Diophantine geometry 4 (2007), 335-361, Ed. Norm., Pisa Zbl1194.13027MR2349665
  13. Oscar Zariski, Studies in equisingularity. I. Equivalent singularities of plane algebroid curves, Amer. J. Math. 87 (1965), 507-536 Zbl0132.41601MR177985
  14. Oscar Zariski, Le problème des modules pour les branches planes, (1973), École Polytechnique Zbl0317.14004MR414561

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