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Minimal characteristic exponent of the Gauss-Manin connection of isolated singular point and Newton polyhedron

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References

  1. Arnol'd, V.I.: Remarks on the stationary phase method and coxeter numbers. Russian Math. Surveys28, 19–48 (1973)

    Google Scholar 

  2. Brieskorn, E.: Die Monodromie der isolierten Singularitäten von Hyperflächen. Manuscripta Math.2, 103–161 (1970)

    Google Scholar 

  3. Deligne, P.: Equations différentielles à point singuliers régulies. In: Lecture Notes in Mathematics. Vol. 163. Berlin, Heidelberg, New York: Springer 1970

    Google Scholar 

  4. Ehlers, F.: Newtonpolyeder und die Monodromie von Hyperflächen-singularitäten. Bonn. Math. Schr.111 (1978).

  5. Griffiths, P.A.: Monodromy of homology and periods of integrals on algebraic manifolds. Princeton: Princeton University Press 1968

    Google Scholar 

  6. Katz, N.M.: The regularity theorem in algebraic geometry. Actes Congr. Int. Math.1, 437–443 (1970)

    Google Scholar 

  7. Kempf, G., Knudsen, F., Mumford, D., Saint-Donat, B.: Toroidal embeddings. I. In: Lecture Notes in Mathematics, Vol. 339. Berlin, Heidelberg, New York: Springer 1973

    Google Scholar 

  8. Khovanskii, A.G.: Newton polyhedra and the genus of complete intersections. Functional Analysis Appl.12, 38–46 (1978)

    Google Scholar 

  9. Lo, K.C.: Exposants de Gauss-Manin. In: Singularité des systèmes différentiels de Gauss-Manin. Progress in Mathematics 2, pp. 171–212. Basel, Boston, Stuttgart: Birkhäuser 1979

    Google Scholar 

  10. Malgrange, B.: Le polynome de Bernstein d'une singulatité isolée. In: Lecture Notes in Mathematics, Vol. 459, pp. 98–119. Berlin, Heidelberg, New York: Springer 1974

    Google Scholar 

  11. Malgrange, B.: Intégrales asymptotiques et monodromic. Ann. Sci. Ecole Norm. Sup.7, 405–430 (1974)

    Google Scholar 

  12. Milnor, J.: Singular points of complex hypersurfaces. Ann. of Math. Studies, No. 61. Princeton: Princeton University Press 1968

    Google Scholar 

  13. Nilsson, N.: Some growth and rainification properties of certain integrals. Arkiv Math.5, 527–540 (1963–1965)

    Google Scholar 

  14. Pham, F.: Singularités des systèmes différentiels de Gauss-Manin. Progress in Mathematics 2. Basel, Boston, Stuttgart: Birkhäuser 1979

    Google Scholar 

  15. Scherk, J.: Isolated singular points and the Gauss-Manin connection. D. Phil Thesis, Exeter College, Oxford (1977)

    Google Scholar 

  16. Scherk, J.: On the Gauss-Manin connection of an isolated hypersurface singularity. Math. Ann.238, 23–32 (1978)

    Google Scholar 

  17. Sébastiani, M.: Preuve d'une conjecture de Brieskorn. Manuscripta Math.2, 301–308 (1970)

    Google Scholar 

  18. Varchenko, A.N.: Zeta-function of monodromy and Newton's diagram. Invent. Math.37, 253–262 (1976)

    Google Scholar 

  19. Varchenko, A.N.: Newton polyhedra and estimation of oscillating integrals. In: Functional Analysis Appl.10, 175–196 (1976)

  20. Varchenko, A.N.: Gauss-Manin connection of isolated singular point and Bernstein polynomial. Bull. Soc. Math.104, 205–223 (1980)

    Google Scholar 

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Authors and Affiliations

  1. Sonderforschungsbereich Theoretische Mathematik, Mathematisches Institut der Universität, Beringstrasse 4, D-5300, Bonn 1, Germany

    Fritz Ehlers & Kam-Chan Lo

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  1. Fritz Ehlers
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  2. Kam-Chan Lo
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This work was done under the program Sonderforschungsbereich “Theoretische Mathematik” (SFB 40) at Bonn University

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Ehlers, F., Lo, KC. Minimal characteristic exponent of the Gauss-Manin connection of isolated singular point and Newton polyhedron. Math. Ann. 259, 431–441 (1982). https://doi.org/10.1007/BF01466050

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