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.
@article{bwmeta1.element.doi-10_2478_s11533-011-0076-1,
author = {Muhammad Banyamin and Gerhard Pfister and Stefan Steidel},
title = {About the computation of the signature of surface singularities z N + g(x, y) = 0},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {271-276},
zbl = {1244.14050},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0076-1}
}
Muhammad Banyamin; Gerhard Pfister; Stefan Steidel. About the computation of the signature of surface singularities z N + g(x, y) = 0. Open Mathematics, Tome 10 (2012) pp. 271-276. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0076-1/
[1] Arnold V.I., Gusein-Zade S.M., Varchenko A.N., Singularities of Differentiable Maps, Vol. 1, 2, Monogr. Math., 82, 83, Birkhäuser, Boston, 1985, 1988 http://dx.doi.org/10.1007/978-1-4612-5154-5
[2] Campillo A., Algebroid Curves in Positive Characteristic, Lecture Notes in Math., 813, Springer, Berlin, 1980 | Zbl 0451.14010
[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] 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 | Zbl 0712.32022
[5] Greuel G.-M., Pfister G., A Singular Introduction to Commutative Algebra, 2nd ed., Springer, Berlin, 2008
[6] de Jong T., Pfister G., Local Analytic Geometry, Adv. Lectures Math., Friedr. Vieweg & Sohn, Braunschweig, 2000
[7] Kerner D., Némethi, A., The Milnor fibre signature is not semi-continous, In: Topology of Algebraic Varieties and Singularities, Contemp. Math., 538, American Mathematical Society, Providence, 2011, 369–376 | Zbl 1225.32030
[8] Kulikov V.S., Mixed Hodge Structures and Singularities, Cambridge Tracts in Math., 132, Cambridge University Press, Cambridge, 1998 | Zbl 0902.14005
[9] Milnor J., Singular Points of Complex Hypersurfaces, Ann. of Math. Stud., 61, Princeton University Press, Princeton, 1968 | Zbl 0184.48405
[10] Némethi A., The real Seifert form and the spectral pairs of isolated hypersurface singularities, Compositio Math., 1995, 98(1), 23–41 | Zbl 0851.14015
[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] 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 | Zbl 0912.32029
[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 | Zbl 0942.14004
[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 | Zbl 0628.32038
[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 | Zbl 0749.14003
[16] Steenbrink J., Intersection form for quasi-homogeneous singularities, Compositio Math., 1977, 34(2), 211–223 | Zbl 0347.14001
[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