Milnor fibration at infinity for mixed polynomials

Ying Chen

Open Mathematics (2014)

  • Volume: 12, Issue: 1, page 28-38
  • ISSN: 2391-5455

Abstract

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We study the existence of Milnor fibration on a big enough sphere at infinity for a mixed polynomial f: ℝ2n → ℝ2. By using strongly non-degenerate condition, we prove a counterpart of Némethi and Zaharia’s fibration theorem. In particular, we obtain a global version of Oka’s fibration theorem for strongly non-degenerate and convenient mixed polynomials.

How to cite

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Ying Chen. "Milnor fibration at infinity for mixed polynomials." Open Mathematics 12.1 (2014): 28-38. <http://eudml.org/doc/269348>.

@article{YingChen2014,
abstract = {We study the existence of Milnor fibration on a big enough sphere at infinity for a mixed polynomial f: ℝ2n → ℝ2. By using strongly non-degenerate condition, we prove a counterpart of Némethi and Zaharia’s fibration theorem. In particular, we obtain a global version of Oka’s fibration theorem for strongly non-degenerate and convenient mixed polynomials.},
author = {Ying Chen},
journal = {Open Mathematics},
keywords = {Fibrations on spheres; Bifurcation locus; Newton polyhedron; Regularity at infinity; Mixed polynomials; Milnor fibration; mixed polynomials},
language = {eng},
number = {1},
pages = {28-38},
title = {Milnor fibration at infinity for mixed polynomials},
url = {http://eudml.org/doc/269348},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Ying Chen
TI - Milnor fibration at infinity for mixed polynomials
JO - Open Mathematics
PY - 2014
VL - 12
IS - 1
SP - 28
EP - 38
AB - We study the existence of Milnor fibration on a big enough sphere at infinity for a mixed polynomial f: ℝ2n → ℝ2. By using strongly non-degenerate condition, we prove a counterpart of Némethi and Zaharia’s fibration theorem. In particular, we obtain a global version of Oka’s fibration theorem for strongly non-degenerate and convenient mixed polynomials.
LA - eng
KW - Fibrations on spheres; Bifurcation locus; Newton polyhedron; Regularity at infinity; Mixed polynomials; Milnor fibration; mixed polynomials
UR - http://eudml.org/doc/269348
ER -

References

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  3. [3] Broughton S.A., On the topology of polynomial hypersurfaces, In: Singularities, Part 1, Arcata, July 20–August 7, 1981, Proc. Sympos. Pure Math., 40, American Mathematical Society, Providence, 1983, 167–178 
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  5. [5] Chen Y., Bifurcation Values of Mixed Polynomials and Newton Polyhedra, PhD thesis, Université de Lille 1, Lille, 2012 
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  7. [7] Cisneros-Molina J.L., Join theorem for polar weighted homogeneous singularities, In: Singularities II, Cuernavaca, January 8–26, 2007, Contemp. Math., 475, American Mathematical Society, Providence, 2008, 43–59 Zbl1172.32008
  8. [8] Kouchnirenko A.G., Polyèdres de Newton et nombres de Milnor, Invent. Math., 1976, 32(1), 1–31 http://dx.doi.org/10.1007/BF01389769 Zbl0328.32007
  9. [9] Milnor J., Singular Points of Complex Hypersurfaces, Ann. of Math. Studies, 61, Princeton University Press, 1968 Zbl0184.48405
  10. [10] Némethi A., Théorie de Lefschetz pour les variétés algébriques affines, C. R. Acad. Sci. Paris Sér. I Math., 1986, 303(12), 567–570 Zbl0612.14007
  11. [11] Némethi A., Lefschetz theory for complex affine varieties, Rev. Roumaine Math. Pures Appl., 1988, 33(3), 233–250 Zbl0665.14003
  12. [12] Némethi A., Zaharia A., On the bifurcation set of a polynomial function and Newton boundary, Publ. Res. Inst. Math. Sci., 1990, 26(4), 681–689 http://dx.doi.org/10.2977/prims/1195170853 Zbl0736.32024
  13. [13] Némethi A., Zaharia A., Milnor fibration at infinity, Indag. Math. (N.S.), 1992, 3(3), 323–335 http://dx.doi.org/10.1016/0019-3577(92)90039-N Zbl0806.57021
  14. [14] Oka M., Topology of polar weighted homogeneous hypersurfaces, Kodai Math. J., 2008, 31(2), 163–182 http://dx.doi.org/10.2996/kmj/1214442793 
  15. [15] Oka M., Non-degenerate mixed functions, Kodai Math. J., 2010, 33(1), 1–62 http://dx.doi.org/10.2996/kmj/1270559157 

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