PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1995 | 31 | 1 | 163-171
Tytuł artykułu

The Jacobian Conjecture: survey of some results

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper contains the formulation of the problem and an almost up-to-date survey of some results in the area.
Słowa kluczowe
Rocznik
Tom
31
Numer
1
Strony
163-171
Opis fizyczny
Daty
wydano
1995
Twórcy
  • Institute of Mathematics, Jagiellonian University, Reymonta 4/508, 30-059 Kraków, Poland
Bibliografia
  • [A] S. S. Abhyankar, Local Analytic Geometry, Academic Press, New York, 1964.
  • [BCW] 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.
  • [BR] A. Białynicki-Birula and M. Rosenlicht, Injective morphisms of real algebraic varieties, Proc. Amer. Math. Soc. 13 (1962), 200-203.
  • [Ch] Nguyen Van Chau, A sufficient condition for injectivity of polynomial maps on $ℝ^2$, Acta Math. Vietnamica, to appear.
  • [CK] J. Chądzyński and T. Krasiński, Properness and the Jacobian Conjecture in $C^2$, Bull. Soc. Sci. Lettres Łódź XIV, 132 (1992), 13-19.
  • [Co] P. M. Cohn, On the structure of the $GL_2$ of a ring, Publ. I.H.E.S. 30 (1966), 365-413.
  • [D1] L. M. Drużkowski, An effective approach to Keller's Jacobian Conjecture, Math. Ann. 264 (1983), 303-313.
  • [D2] L. M. Drużkowski, A geometric approach to the Jacobian Conjecture in $C^2$, Ann. Polon. Math. 55 (1991), 95-101.
  • [D3] L. M. Drużkowski, The Jacobian Conjecture in case of rank or corank less than three, J. Pure Appl. Algebra 85 (1993), 233-244.
  • [D4] L. M. Drużkowski, The Jacobian Conjecture, preprint 492, Institute of Mathematics, Polish Academy of Sciences, Warsaw, 1991.
  • [DR] L. M. Drużkowski and K. Rusek, The formal inverse and the Jacobian Conjecture, Ann. Polon. Math. 46 (1985), 85-90.
  • [DT] L. M. Drużkowski and H. Tutaj, Differential conditions to verify the Jacobian Conjecture, ibid. 57 (1992), 253-263.
  • [E] W. Engel, Ein Satz über ganze Cremona Transformationen der Ebene, Math. Ann. 130 (1955), 11-19.
  • [Es1] A. van den Essen, A criterion to decide if a polynomial map is invertible and to compute the inverse, Comm. Algebra 18 (1990), 3183-3186.
  • [Es2] A. van den Essen, Polynomial maps and the Jacobian Conjecture, Report 9034, Catholic University, Nijmegen, The Netherlands, 1990.
  • [Es3] A. van den Essen, The exotic world of invertible polynomial maps, Nieuw Arch. Wisk. (4) 11 (1993), 21-31.
  • [G] W. Gröbner, Sopra un teorema di B. Segre, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. 31 (1961), 118-122.
  • [K] O.-H. Keller, Ganze Cremona-Transformationen, Monatshefte Math. Phys. 47 (1939), 299-306.
  • [KS] T. Krasiński and S. Spodzieja, On linear differential operators related to the n-dimensional Jacobian Conjecture, in: Lecture Notes Math. 1524, Springer, 1992, 308-315.
  • [M] G. H. Meisters, Jacobian problems in differential equations and algebraic geometry, Rocky Mountain J. Math. 12 (1982), 679-705.
  • [MO1] G. H. Meisters and C. Olech, A poly-flow formulation of the Jacobian Conjecture, Bull. Polish Acad. Sci. 35 (1987), 725-731.
  • [MO2] G. H. Meisters and C. Olech, Solution of the Global Asymptotic Stability Jacobian Conjecture for the polynomial case, in: Analyse Mathématique et Applications, Gauthier-Villars, Paris, 1988, 373-381.
  • [MO3] G. H. Meisters and C. Olech, A Jacobian Condition for injectivity of differentiable plane maps, Ann. Polon. Math. 51 (1990), 249-254.
  • [Mo] T. T. Moh, On the Jacobian Conjecture and the configuration of roots, J. Reine Angew. Math. 340 (1983), 140-212.
  • [O] S. Oda, The Jacobian Problem and the simply-connectedness of $A^n$ over a field k of characteristic zero, preprint, Osaka University, 1980.
  • [Or] S. Yu. Orevkov, On three-sheeted polynomial mappings of $C^2$, Izv. Akad. Nauk SSSR 50 (6) (1986), 1231-1240 (in Russian).
  • [P] A. Płoski, On the growth of proper polynomial mappings, Ann. Polon. Math. 45 (1985), 297-309.
  • [R1] K. Rusek, A geometric approach to Keller's Jacobian Conjecture, Math. Ann. 264 (1983), 315-320.
  • [R2] K. Rusek, Polynomial automorphisms, preprint 456, Institute of Mathematics, Polish Academy of Sciences, Warsaw, 1989.
  • [RW] K. Rusek and T. Winiarski, Polynomial automorphisms of $C^n$, Univ. Iagell. Acta Math. 24 (1984), 143-149.
  • [S1] B. Segre, Corrispondenze di Möbius e Transformazioni cremoniane intere, Atti Accad. Sci. Torino: Cl. Sci. Fis. Mat. Nat. 91 (1956-57), 3-19.
  • [S2] B. Segre, Forma differenziali e loro integrali, vol. II, Docet, Roma, 1956.
  • [S3] B. Segre, Variazione continua ed omotopia in geometria algebraica, Ann. Mat. Pura Appl. 100 (1960), 149-186.
  • [St] B. Segre, On linear differential operators related to the Jacobian Conjecture, J. Pure Appl. Algebra 52 (1989), 175-186.
  • [V] A. G. Vitushkin, Some examples connected with polynomial mappings in $ℂ^n$, Izv. Akad. Nauk SSSR Ser. Mat. 35 (2) (1971), 269-279.
  • [W] T. Winiarski, Inverse of polynomial automorphisms of $ℂ^n$, Bull. Acad. Polon. Sci. Math. 27 (1979), 673-674.
  • [Wr1] D. Wright, The amalgamated free product structure of $GL_2(k[X_1,...,X_n])$ and the weak Jacobian Theorem for two variables, J. Pure Appl. Algebra 12 (1978), 235-251.
  • [Wr2] D. Wright, The Jacobian Conjecture: linear triangularization for cubics in dimension three, Linear and Multilinear Algebra 34 (1993), 85-97.
  • [Y] A. V. Yagzhev, On Keller's problem, Sibirsk. Mat. Zh. 21 (1980), 141-150 (in Russian).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv31z1p163bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.