ArticleOriginal scientific text
Title
Jung's type theorem for polynomial transformations of ℂ²
Authors 1
Affiliations
- Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Kraków, Poland
Abstract
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 + terms of degree < m+n.
Bibliography
- S. S. Abhyankar, Expansion Techniques in Algebraic Geometry, Tata Inst. Fund. Research, Bombay 1977.
- 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.
- R. C. Heitmann, On the Jacobian Conjecture, J. Pure Appl. Algebra 64 (1990), 35-72.
- H. W. E. Jung, Über ganze birationale Transformationen der Ebene, J. Reine Angew. Math. 184 (1942), 161-174.
- O.-H. Keller, Ganze Cremona-Transformationen, Monatsh. Math. Phys. 47 (1939), 299-306.
- L. G. Makar-Limanov, On automorphisms of the free algebra on two generators, Funktsional. Anal. i Prilozhen. 4 (3) (1970), 107-108 (in Russian).
- K. Rusek, Polynomial automorphisms, preprint 456, IM PAN, 1989.
- A. G. Vitushkin, On polynomial transformations of
, in: Manifolds, Tokyo 1973, Univ. of Tokyo Press, 1975, 415-417.