The set of points at which a polynomial map is not proper
Zbigniew Jelonek
Annales Polonici Mathematici, Tome 58 (1993), p. 259-266 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

We describe the set of points over which a dominant polynomial map f=(f1,...,fn):ℂn→ℂn is not a local analytic covering. We show that this set is either empty or it is a uniruled hypersurface of degree bounded by (∏i=1ndegfi-μ(f))/(mini=1,...,ndegfi).

Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:262458 
@article{bwmeta1.element.bwnjournal-article-apmv58z3p259bwm,
     author = {Zbigniew Jelonek},
     title = {The set of points at which a polynomial map is not proper},
     journal = {Annales Polonici Mathematici},
     volume = {58},
     year = {1993},
     pages = {259-266},
     zbl = {0806.14009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv58z3p259bwm}
}

Zbigniew Jelonek. The set of points at which a polynomial map is not proper. Annales Polonici Mathematici, Tome 58 (1993) pp. 259-266. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv58z3p259bwm/

[000] [1] Z. Jelonek, The extension of regular and rational embeddings, Math. Ann. 277 (1987), 113-120. | Zbl 0611.14010

[001] [2] Z. Jelonek, Irreducible identity sets for polynomial automorphisms, Math. Z. 212 (1993), 601-617. | Zbl 0806.14011

[002] [3] Z. Jelonek, The set of points at which a polynomial map is not proper, preprint CRM no. 141, Bellaterra, March 1992.

[003] [4] M. Kwieciński, Extending finite mappings to affine spaces, J. Pure Appl. Algebra 76 (1991), 151-154. | Zbl 0753.14002

[004] [5] D. Mumford, Algebraic Geometry I, Springer, Berlin, 1976. | Zbl 0356.14002

[005] [6] O. Perron, Algebra I (Die Grundlagen), Göschens Lehrbücherei, Berlin und Leipzig, 1932.

[006] [7] A. Płoski, Algebraic dependence and polynomial automorphisms, Bull. Polish Acad. Sci. Math. 34 (1986), 653-659. | Zbl 0616.32006

[007] [8] A. Płoski, On the growth of proper polynomial mappings, Ann. Polon. Math. 45 (1985), 297-309. | Zbl 0584.32006

[008] [9] I. R. Shafarevich, Basic Algebraic Geometry, Springer, 1974. | Zbl 0284.14001

[009] [10] P. Tworzewski and T. Winiarski, Analytic sets with proper projections, J. Reine Angew. Math. 337 (1982), 68-76. | Zbl 0497.32024