Jung's type theorem for polynomial transformations of ℂ²

• Autorzy: Sławomir Kołodziej
• Języki publikacji: EN

Abstrakty

EN

We prove that among counterexamples to the Jacobian Conjecture, if there are any, we can find one of lowest degree, the coordinates of which have the form $x^m y^n$ + terms of degree < m+n.

Kategorie tematyczne

• 32N05: General theory of automorphic functions of several complex variables

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1991
• Tom: 55
• Numer: 1
• Strony: 207-212

Daty

wydano

1991

otrzymano

1990-08-25

Twórcy

autor

Sławomir Kołodziej

• Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Kraków, Poland

Bibliografia

• [1] S. S. Abhyankar, Expansion Techniques in Algebraic Geometry, Tata Inst. Fund. Research, Bombay 1977.
• [2] 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 (2) (1982), 287-330.
• [3] R. C. Heitmann, On the Jacobian Conjecture, J. Pure Appl. Algebra 64 (1990), 35-72.
• [4] H. W. E. Jung, Über ganze birationale Transformationen der Ebene, J. Reine Angew. Math. 184 (1942), 161-174.
• [5] O.-H. Keller, Ganze Cremona-Transformationen, Monatsh. Math. Phys. 47 (1939), 299-306.
• [6] L. G. Makar-Limanov, On automorphisms of the free algebra on two generators, Funktsional. Anal. i Prilozhen. 4 (3) (1970), 107-108 (in Russian).
• [7] K. Rusek, Polynomial automorphisms, preprint 456, IM PAN, 1989.
• [8] A. G. Vitushkin, On polynomial transformations of $ℂ^n$, in: Manifolds, Tokyo 1973, Univ. of Tokyo Press, 1975, 415-417.