# Jung's type theorem for polynomial transformations of ℂ²

Annales Polonici Mathematici (1991)

- Volume: 55, Issue: 1, page 207-212
- ISSN: 0066-2216

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topSławomir Kołodziej. "Jung's type theorem for polynomial transformations of ℂ²." Annales Polonici Mathematici 55.1 (1991): 207-212. <http://eudml.org/doc/262440>.

@article{SławomirKołodziej1991,

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 $x^m y^n$ + terms of degree < m+n.},

author = {Sławomir Kołodziej},

journal = {Annales Polonici Mathematici},

keywords = {Jacobian conjecture; birational automorphisms; polynomial automorphism},

language = {eng},

number = {1},

pages = {207-212},

title = {Jung's type theorem for polynomial transformations of ℂ²},

url = {http://eudml.org/doc/262440},

volume = {55},

year = {1991},

}

TY - JOUR

AU - Sławomir Kołodziej

TI - Jung's type theorem for polynomial transformations of ℂ²

JO - Annales Polonici Mathematici

PY - 1991

VL - 55

IS - 1

SP - 207

EP - 212

AB - 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.

LA - eng

KW - Jacobian conjecture; birational automorphisms; polynomial automorphism

UR - http://eudml.org/doc/262440

ER -

## References

top- [1] S. S. Abhyankar, Expansion Techniques in Algebraic Geometry, Tata Inst. Fund. Research, Bombay 1977. Zbl0818.14001
- [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. Zbl0539.13012
- [3] R. C. Heitmann, On the Jacobian Conjecture, J. Pure Appl. Algebra 64 (1990), 35-72. Zbl0704.13010
- [4] H. W. E. Jung, Über ganze birationale Transformationen der Ebene, J. Reine Angew. Math. 184 (1942), 161-174. Zbl0027.08503
- [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 ${\u2102}^{n}$, in: Manifolds, Tokyo 1973, Univ. of Tokyo Press, 1975, 415-417.

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