Finite extensions of mappings from a smooth variety

Marek Karaś

Annales Polonici Mathematici (2000)

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

Abstract

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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.

How to cite

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Karaś, 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

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

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