# Finite extensions of mappings from a smooth variety

Annales Polonici Mathematici (2000)

- Volume: 75, Issue: 1, page 79-86
- ISSN: 0066-2216

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topKaraś, Marek. "Finite extensions of mappings from a smooth variety." Annales Polonici Mathematici 75.1 (2000): 79-86. <http://eudml.org/doc/208386>.

@article{Karaś2000,

abstract = {Let V, W be algebraic subsets of $k^n$, $k^m$ respectively, with n ≤ m. It is known that any finite polynomial mapping f: V → W can be extended to a finite polynomial mapping $F: k^\{n\} → k^\{m\}.$ The main goal of this paper is to estimate from above the geometric degree of a finite extension $F: k^n → k^n$ of a dominating mapping f: V → W, where V and W are smooth algebraic sets.},

author = {Karaś, Marek},

journal = {Annales Polonici Mathematici},

keywords = {finite extension; geometric degree; finite mapping; finite polynomial mapping; degree},

language = {eng},

number = {1},

pages = {79-86},

title = {Finite extensions of mappings from a smooth variety},

url = {http://eudml.org/doc/208386},

volume = {75},

year = {2000},

}

TY - JOUR

AU - Karaś, Marek

TI - Finite extensions of mappings from a smooth variety

JO - Annales Polonici Mathematici

PY - 2000

VL - 75

IS - 1

SP - 79

EP - 86

AB - Let V, W be algebraic subsets of $k^n$, $k^m$ respectively, with n ≤ m. It is known that any finite polynomial mapping f: V → W can be extended to a finite polynomial mapping $F: k^{n} → k^{m}.$ The main goal of this paper is to estimate from above the geometric degree of a finite extension $F: k^n → k^n$ of a dominating mapping f: V → W, where V and W are smooth algebraic sets.

LA - eng

KW - finite extension; geometric degree; finite mapping; finite polynomial mapping; degree

UR - http://eudml.org/doc/208386

ER -

## References

top- [1] S. S. Abhyankar, On the Semigroup of a Meromorphic Curve, Kinokuniya Book-Store, Tokyo, 1978.
- [2] Z. Jelonek, The extension of regular and rational embeddings, Math. Ann. 277 (1987), 113-120. Zbl0611.14010
- [3] M. Karaś, An estimation of the geometric degree of an extension of some polynomial proper mappings, Univ. Iagell. Acta Math. 35 (1997), 131-135. Zbl0948.14015
- [4] M. Karaś, Geometric degree of finite extensions of projections, ibid. 37 (1999), 109-119. Zbl0989.14020
- [5] M. Karaś, Birational finite extensions, J. Pure Appl. Algebra 148 (2000), 251-253. Zbl1014.14003
- [6] M. Kwieciński, Extending finite mappings to affine space, ibid. 76 (1991), 151-153. Zbl0753.14002
- [7] D. Mumford, Algebraic Geometry I. Complex Projective Varieties, Springer, Heidelberg, 1976. Zbl0356.14002
- [8] K. J. Nowak, The extension of holomorphic functions of polynomial growth on algebraic sets in ${\u2102}^{n}$, Univ. Iagell. Acta Math. 28 (1991), 19-28.
- [9] I. R. Shafarevich, Basic Algebraic Geometry, Springer, Heidelberg, 1974. Zbl0284.14001

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