Finite extensions of mappings from a smooth variety

• Autorzy: Marek Karaś
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

finite extension; geometric degree; finite mapping

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2000
• Tom: 75
• Numer: 1
• Strony: 79-86

Daty

wydano

2000

otrzymano

1999-12-22

poprawiono

2000-04-04

Twórcy

autor

Marek Karaś

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Bibliografia

• [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.
• [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.
• [4] M. Karaś, Geometric degree of finite extensions of projections, ibid. 37 (1999), 109-119.
• [5] M. Karaś, Birational finite extensions, J. Pure Appl. Algebra 148 (2000), 251-253.
• [6] M. Kwieciński, Extending finite mappings to affine space, ibid. 76 (1991), 151-153.
• [7] D. Mumford, Algebraic Geometry I. Complex Projective Varieties, Springer, Heidelberg, 1976.
• [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] I. R. Shafarevich, Basic Algebraic Geometry, Springer, Heidelberg, 1974.