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1999 | 72 | 3 | 219-249
Tytuł artykułu

Monodromy, differential equations and the Jacobian conjecture

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study certain problems on polynomial mappings related to the Jacobian conjecture.
Rocznik
Tom
72
Numer
3
Strony
219-249
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-09-24
poprawiono
1999-04-30
Twórcy
  • Department of Mathematics, Statistics, and Computer Science, University of Illinois-Chicago, 851 S. Morgan, Chicago, IL 60607-7045, U.S.A.
Bibliografia
  • [A-C-D] E. Artal-Bartolo, P. Cassou-Noguès et A. Dimca, Sur la topologie des polynômes complexes, in: Progr. Math. 162, Birkhäuser, 1998, 317-343.
  • [Bai] G. Bailly-Maitre, Sur le système local de Gauss-Manin d'un polynôme de deux variables, preprint, 1998.
  • [B-C-W] H. Bass, E. H. Connell and D. Wright, The Jacobian Conjecture: Reduction of degree and formal expansion of the inverse, Bull. Amer. Math. Soc. 7 (1982), 287-330.
  • [B-N] S. R. Bell and R. Narasimhan, Proper holomorphic mappings of complex spaces, in: Complex Manifolds, S. R. Bell et al. (eds.), Springer, 1998, 1-38.
  • [Del1] P. Deligne, Equations Différentielles à Points Singuliers Réguliers, Lecture Notes in Math. 163, Springer, 1970.
  • [Del2] P. Deligne, Théorie de Hodge, II, Publ. Math. I.H.E.S. 40 (1971), 5-58.
  • [Dim] A. Dimca, Invariant cycles for complex polynomials, Rev. Roumaine Math. Pures Appl. 43 (1998), 113-120.
  • [Dru] L. M. Drużkowski, The Jacobian conjecture: some steps towards solution, in: Automorphisms of Affine Spaces, A. van den Essen (ed.), Kluwer, 1995, 41-54.
  • [Ess] A. van den Essen, Polynomial automorphisms and the Jacobian conjecture, in: Algèbre non commutative, groupes quantiques et invariants (Reims, 1995), J. Alev and G. Cauchon (eds.), Soc. Math. France, Paris, 1997, 55-81.
  • [F-K] H. M. Farkas and I. Kra, Riemann Surfaces, Springer, 1980.
  • [For1] O. Forster, Some remarks on parallelizable Stein manifolds, Bull. Amer. Math. Soc. 73 (1967), 712-716.
  • [For2] O. Forster, Plongements de variétés de Stein, Comment. Math. Helv. 45 (1970), 170-184.
  • [Fri] S. Friedland, On the plane Jacobian conjecture, preprint, IHES, 1994.
  • [G-R] H. Grauert and R. Remmert, Coherent Analytic Sheaves, Springer, 1984.
  • [Gri] P. Griffiths, Periods of integrals on algebraic manifolds: summary of main results and discussion of open problems, Bull. Amer. Math. Soc. 76 (1970), 228-296.
  • [G-H] P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley, 1978.
  • [Gro] A. Grothendieck, On the de Rham cohomology of algebraic varieties, Publ. Math. I.H.E.S. 29 (1966), 351-359.
  • [Hei] R. C. Heitmann, On the Jacobian conjecture, J. Pure Appl. Algebra 64 (1990), 35-72; Corrigendum, ibid. 90 (1993), 199-200.
  • [Kal] S. Kaliman, On the Jacobian Conjecture, Proc. Amer. Math. Soc. 117 (1993), 45-51.
  • [Kol] F. R. Kolchin, Differential Algebra and Algebraic Groups, Academic Press, 1973.
  • [K-S] T. Krasiński and S. Spodzieja, On linear differential operators related to the n-dimensional jacobian conjecture, in: Real Algebraic Geometry, M. Coste, L. Mahé and M.-F. Roy (eds.), Lecture Notes in Math. 1524, Springer, 1992, 308-315.
  • [L-W] Lê Dung Trang et C. Weber, Polynômes à fibrés rationnelles et conjecture jacobienne à 2 variables, C. R. Acad. Sci. Paris 320 (1995), 581-584.
  • [Lib1] A. Libgober, Alexander polynomial of plane algebraic curves and cyclic multiple planes, Duke Math. J. 49 (1982), 833-851.
  • [Lib2] A. Libgober, On the homotopy type of the complement to plane algebraic curves, J. Reine Angew. Math. 367 (1986), 103-114.
  • [Mal] B. Malgrange, Intégrales asymptotiques et monodromie, Ann. Sci. École Norm. Sup. 7 (1974), 405-430.
  • [Mil] J. Milnor, Singular Points of Complex Hypersurfaces, Princeton Univ. Press, 1968.
  • [Nag] S. Nag, The Complex Analytic Theory of Teichmüller Spaces, Wiley, 1988.
  • [N-S] P. Nousiainen and M. E. Sweedler, Automorphisms of polynomial and power series rings, J. Pure Appl. Algebra 29 (1983), 93-97.
  • [Ore] S. Yu. Orevkov, On three-sheeted polynomial mappings of ℂ², Math. USSR-Izv. 29 (1987), 587-596.
  • [Raz] M. Razar, Polynomial maps with constant jacobian, Israel J. Math. 32 (1979), 97-106.
  • [Sma] S. Smale, Mathematical problems for the next century, Math. Intelligencer 20 (1998), no. 2, 7-15.
  • [Ste1] Y. Stein, The total reducibility order of a polynomial in two variables, Israel J. Math. 68 (1989), 109-122.
  • [Ste2] Y. Stein, On the density of image of differential operators generated by polynomials, J. Anal. Math. 52 (1989), 291-300.
  • [Suz] M. Suzuki, Propriétés topologiques des polynômes de deux variables complexes, et automorphismes algébriques de l'espace ℂ², J. Math. Soc. Japan 26 (1974), 241-257.
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Bibliografia
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