About the computation of the signature of surface singularities z N + g(x, y) = 0

Muhammad Banyamin; Gerhard Pfister; Stefan Steidel

Open Mathematics (2012)

  • Volume: 10, Issue: 1, page 271-276
  • ISSN: 2391-5455

Abstract

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In this article we describe our experiences with a parallel Singular implementation of the signature of a surface singularity defined by z N + g(x; y) = 0.

How to cite

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Muhammad Banyamin, Gerhard Pfister, and Stefan Steidel. "About the computation of the signature of surface singularities z N + g(x, y) = 0." Open Mathematics 10.1 (2012): 271-276. <http://eudml.org/doc/269617>.

@article{MuhammadBanyamin2012,
abstract = {In this article we describe our experiences with a parallel Singular implementation of the signature of a surface singularity defined by z N + g(x; y) = 0.},
author = {Muhammad Banyamin, Gerhard Pfister, Stefan Steidel},
journal = {Open Mathematics},
keywords = {Signature; Surface singularity; Intersection form; Seifert form; eta-invariant; signature; surface singularity; intersection form},
language = {eng},
number = {1},
pages = {271-276},
title = {About the computation of the signature of surface singularities z N + g(x, y) = 0},
url = {http://eudml.org/doc/269617},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Muhammad Banyamin
AU - Gerhard Pfister
AU - Stefan Steidel
TI - About the computation of the signature of surface singularities z N + g(x, y) = 0
JO - Open Mathematics
PY - 2012
VL - 10
IS - 1
SP - 271
EP - 276
AB - In this article we describe our experiences with a parallel Singular implementation of the signature of a surface singularity defined by z N + g(x; y) = 0.
LA - eng
KW - Signature; Surface singularity; Intersection form; Seifert form; eta-invariant; signature; surface singularity; intersection form
UR - http://eudml.org/doc/269617
ER -

References

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  2. [2] Campillo A., Algebroid Curves in Positive Characteristic, Lecture Notes in Math., 813, Springer, Berlin, 1980 Zbl0451.14010
  3. [3] Decker W., Greuel G.-M., Pfister G., Schönemann H., Singular 3-1-3 - A computer algebra system for polynomial computations, 2011, http://www.singular.uni-kl.de 
  4. [4] van Doorn M.G.M., Steenbrink J.H.M., A supplement to the monodromy theorem, Abh. Math. Sem. Univ. Hamburg, 1989, 59, 225–233 http://dx.doi.org/10.1007/BF02942330 Zbl0712.32022
  5. [5] Greuel G.-M., Pfister G., A Singular Introduction to Commutative Algebra, 2nd ed., Springer, Berlin, 2008 
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  8. [8] Kulikov V.S., Mixed Hodge Structures and Singularities, Cambridge Tracts in Math., 132, Cambridge University Press, Cambridge, 1998 Zbl0902.14005
  9. [9] Milnor J., Singular Points of Complex Hypersurfaces, Ann. of Math. Stud., 61, Princeton University Press, Princeton, 1968 Zbl0184.48405
  10. [10] Némethi A., The real Seifert form and the spectral pairs of isolated hypersurface singularities, Compositio Math., 1995, 98(1), 23–41 Zbl0851.14015
  11. [11] Némethi A., The equivariant signature of hypersurface singularities and eta-invariant, Topology, 1995, 34(2), 243–259 http://dx.doi.org/10.1016/0040-9383(94)00031-F 
  12. [12] Némethi A., Dedekind sums and the signature of f(x; y) + z N, Selecta Math., 1998, 4(2), 361–376 http://dx.doi.org/10.1007/s000290050035 Zbl0912.32029
  13. [13] Némethi A., The signature of f(x; y)+z N, In: Singularity Theory, Liverpool, August 1996, London Math. Soc. Lecture Note Ser., 263, Cambridge University Press, Cambridge, 1999, 131–149 Zbl0942.14004
  14. [14] Saito M., Exponents and Newton polyhedra of isolated hypersurface singularities, Math. Ann., 1988, 281(3), 411–417 http://dx.doi.org/10.1007/BF01457153 Zbl0628.32038
  15. [15] Schrauwen R., Steenbrink J., Stevens J., Spectral pairs and the topology of curve singularities, In: Complex Geometry and Lie Theory, Sundance, 1989, Proc. Sympos. Pure Math., 53, American Mathematical Society, Providence, 1991, 305–328 Zbl0749.14003
  16. [16] Steenbrink J., Intersection form for quasi-homogeneous singularities, Compositio Math., 1977, 34(2), 211–223 Zbl0347.14001
  17. [17] Steenbrink J.H.M., Mixed Hodge structure on the vanishing cohomology, In: Real and Complex Singularities, Proc. Nordic Summer School/NAVF Sympos. Math., Oslo, 1976, Sijthoff & Noordhoff, Alphen aan den Rijn, 1977, 525–563 http://dx.doi.org/10.1007/978-94-010-1289-8_15 

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