Milnor fibration at infinity for mixed polynomials

• Autorzy: Ying Chen
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Fibrations on spheres; Bifurcation locus; Newton polyhedron; Regularity at infinity; Mixed polynomials

Kategorie tematyczne

• 32S20: Global theory of singularities; cohomological properties
• 58K15: Topological properties of mappings
• 57R45: Singularities of differentiable mappings
• 14P10: Semialgebraic sets and related spaces
• 58K05: Critical points of functions and mappings
• 14D06: Fibrations, degenerations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 1
• Strony: 28-38

Daty

wydano

2014-01-01

online

2013-10-30

Twórcy

autor

Ying Chen

• Université Lille 1

Bibliografia

• [1] Araújo dos Santos R.N., Chen Y., Tibăr M., Singular open book structures from real mappings, Cent. Eur. J. Math., 2013, 11(5), 817–828 http://dx.doi.org/10.2478/s11533-013-0212-1
• [2] Bodin A., Milnor fibration and fibred links at infinity, Internat. Math. Res. Notices, 1999, 11, 615–621 http://dx.doi.org/10.1155/S1073792899000318
• [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
• [4] Broughton S.A., Milnor numbers and the topology of polynomial hypersurfaces, Invent. Math., 1988, 92(2), 217–241 http://dx.doi.org/10.1007/BF01404452
• [5] Chen Y., Bifurcation Values of Mixed Polynomials and Newton Polyhedra, PhD thesis, Université de Lille 1, Lille, 2012
• [6] Chen Y., Tibăr M., Bifurcation values and monodromy of mixed polynomials, Math. Res. Lett., 2012, 19(1), 59–79 http://dx.doi.org/10.4310/MRL.2012.v19.n1.a6
• [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
• [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
• [9] Milnor J., Singular Points of Complex Hypersurfaces, Ann. of Math. Studies, 61, Princeton University Press, 1968
• [10] Némethi A., Théorie de Lefschetz pour les variétés algébriques affines, C. R. Acad. Sci. Paris Sér. I Math., 1986, 303(12), 567–570
• [11] Némethi A., Lefschetz theory for complex affine varieties, Rev. Roumaine Math. Pures Appl., 1988, 33(3), 233–250
• [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
• [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
• [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] Oka M., Non-degenerate mixed functions, Kodai Math. J., 2010, 33(1), 1–62 http://dx.doi.org/10.2996/kmj/1270559157

Identyfikatory

DOI

10.2478/s11533-013-0293-x