The jump of the Milnor number in the X 9 singularity class

Szymon Brzostowski; Tadeusz Krasiński

Open Mathematics (2014)

  • Volume: 12, Issue: 3, page 429-435
  • ISSN: 2391-5455

Abstract

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The jump of the Milnor number of an isolated singularity f 0 is the minimal non-zero difference between the Milnor numbers of f 0 and one of its deformations (f s). We prove that for the singularities in the X 9 singularity class their jumps are equal to 2.

How to cite

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Szymon Brzostowski, and Tadeusz Krasiński. "The jump of the Milnor number in the X 9 singularity class." Open Mathematics 12.3 (2014): 429-435. <http://eudml.org/doc/269289>.

@article{SzymonBrzostowski2014,
abstract = {The jump of the Milnor number of an isolated singularity f 0 is the minimal non-zero difference between the Milnor numbers of f 0 and one of its deformations (f s). We prove that for the singularities in the X 9 singularity class their jumps are equal to 2.},
author = {Szymon Brzostowski, Tadeusz Krasiński},
journal = {Open Mathematics},
keywords = {Milnor number; Singularity; Deformation of singularity; singularity; deformation of singularity},
language = {eng},
number = {3},
pages = {429-435},
title = {The jump of the Milnor number in the X 9 singularity class},
url = {http://eudml.org/doc/269289},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Szymon Brzostowski
AU - Tadeusz Krasiński
TI - The jump of the Milnor number in the X 9 singularity class
JO - Open Mathematics
PY - 2014
VL - 12
IS - 3
SP - 429
EP - 435
AB - The jump of the Milnor number of an isolated singularity f 0 is the minimal non-zero difference between the Milnor numbers of f 0 and one of its deformations (f s). We prove that for the singularities in the X 9 singularity class their jumps are equal to 2.
LA - eng
KW - Milnor number; Singularity; Deformation of singularity; singularity; deformation of singularity
UR - http://eudml.org/doc/269289
ER -

References

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  1. [1] Arnold V.I., Gusein-Zade S.M., Varchenko A.N., Singularities of Differentiable Maps, I, Monogr. Math., 82, Birkhäuser, Boston, 1985 http://dx.doi.org/10.1007/978-1-4612-5154-5[Crossref] 
  2. [2] Bodin A., Jump of Milnor numbers, Bull. Braz. Math. Soc. (N.S.), 2007, 38(3), 389–396 http://dx.doi.org/10.1007/s00574-007-0051-4[Crossref] Zbl1131.32015
  3. [3] Ebeling W., Functions of Several Complex Variables and their Singularities, Grad. Stud. Math., 83, American Mathematical Society, Providence, 2007 
  4. [4] Greuel G.-M., Lossen C., Shustin E., Introduction to Singularities and Deformations, Springer Monogr. Math., Springer, Berlin, 2007 Zbl1125.32013
  5. [5] Gwoździewicz J., Płoski A., Formulae for the singularities at infinity of plane algebraic curves, Univ. Iagel. Acta Math., 2001, 39, 109–133 Zbl1015.32026
  6. [6] Gusein-Zade S.M., On singularities from which an A 1 can be split off, Funct. Anal. Appl., 1993, 27(1), 57–59 http://dx.doi.org/10.1007/BF01768670[Crossref] 
  7. [7] Kouchnirenko A.G., Polyèdres de Newton et nombres de Milnor, Invent. Math., 1976, 32(1), 1–31 http://dx.doi.org/10.1007/BF01389769[Crossref] Zbl0328.32007
  8. [8] Martinet J., Singularities of Smooth Functions and Maps London, Math. Soc. Lecture Note Ser., 58, Cambridge University Press, Cambridge, 1982 Zbl0522.58006
  9. [9] Płoski A., Newton polygons and the Łojasiewicz exponent of a holomorphic mapping of C 2, Ann. Polon. Math., 1990, 51, 275–281 Zbl0764.32012
  10. [10] Płoski A., Milnor number of a plane curve and Newton polygons, Univ. Iagel. Acta Math., 1999, 37, 75–80 Zbl0997.32021
  11. [11] Walewska J., The second jump of Milnor numbers, Demonstratio Math., 2010, 43(2), 361–374 Zbl1202.32024
  12. [12] Wall C.T.C., Finite determinacy of smooth map-germs, Bull. London Math. Soc., 1981, 13(6), 481–539 http://dx.doi.org/10.1112/blms/13.6.481[Crossref] 

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