# The set of points at which a polynomial map is not proper

Annales Polonici Mathematici (1993)

- Volume: 58, Issue: 3, page 259-266
- ISSN: 0066-2216

## Access Full Article

top## Abstract

top## How to cite

topZbigniew Jelonek. "The set of points at which a polynomial map is not proper." Annales Polonici Mathematici 58.3 (1993): 259-266. <http://eudml.org/doc/262458>.

@article{ZbigniewJelonek1993,

abstract = {We describe the set of points over which a dominant polynomial map $f=(f_1,...,f_n) : ℂ^n → ℂ^n$ is not a local analytic covering. We show that this set is either empty or it is a uniruled hypersurface of degree bounded by $(∏_\{i=1\}^n deg f_i - μ (f)) / (min_\{i=1,...,n\} deg f_i)$.},

author = {Zbigniew Jelonek},

journal = {Annales Polonici Mathematici},

keywords = {polynomial mappings; proper mappings; dominant mappings; analytic covering; proper map; dominating polynomial map; uniruled hypersurface},

language = {eng},

number = {3},

pages = {259-266},

title = {The set of points at which a polynomial map is not proper},

url = {http://eudml.org/doc/262458},

volume = {58},

year = {1993},

}

TY - JOUR

AU - Zbigniew Jelonek

TI - The set of points at which a polynomial map is not proper

JO - Annales Polonici Mathematici

PY - 1993

VL - 58

IS - 3

SP - 259

EP - 266

AB - We describe the set of points over which a dominant polynomial map $f=(f_1,...,f_n) : ℂ^n → ℂ^n$ is not a local analytic covering. We show that this set is either empty or it is a uniruled hypersurface of degree bounded by $(∏_{i=1}^n deg f_i - μ (f)) / (min_{i=1,...,n} deg f_i)$.

LA - eng

KW - polynomial mappings; proper mappings; dominant mappings; analytic covering; proper map; dominating polynomial map; uniruled hypersurface

UR - http://eudml.org/doc/262458

ER -

## References

top- [1] Z. Jelonek, The extension of regular and rational embeddings, Math. Ann. 277 (1987), 113-120. Zbl0611.14010
- [2] Z. Jelonek, Irreducible identity sets for polynomial automorphisms, Math. Z. 212 (1993), 601-617. Zbl0806.14011
- [3] Z. Jelonek, The set of points at which a polynomial map is not proper, preprint CRM no. 141, Bellaterra, March 1992.
- [4] M. Kwieciński, Extending finite mappings to affine spaces, J. Pure Appl. Algebra 76 (1991), 151-154. Zbl0753.14002
- [5] D. Mumford, Algebraic Geometry I, Springer, Berlin, 1976. Zbl0356.14002
- [6] O. Perron, Algebra I (Die Grundlagen), Göschens Lehrbücherei, Berlin und Leipzig, 1932.
- [7] A. Płoski, Algebraic dependence and polynomial automorphisms, Bull. Polish Acad. Sci. Math. 34 (1986), 653-659. Zbl0616.32006
- [8] A. Płoski, On the growth of proper polynomial mappings, Ann. Polon. Math. 45 (1985), 297-309. Zbl0584.32006
- [9] I. R. Shafarevich, Basic Algebraic Geometry, Springer, 1974. Zbl0284.14001
- [10] P. Tworzewski and T. Winiarski, Analytic sets with proper projections, J. Reine Angew. Math. 337 (1982), 68-76. Zbl0497.32024

## Citations in EuDML Documents

top- Zbigniew Jelonek, Local characterization of algebraic manifolds and characterization of components of the set ${S}_{f}$
- Anna Valette, Guillaume Valette, On the geometry of polynomial mappings at infinity
- A. Fabianom, G. Pucci, A. Yger, Effective Nullstellensatz and geometric degree for zero-dimensional ideals

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.