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Abstrakty
We present an example of finite mappings of algebraic varieties ƒ : V → W, where V ⊂ kn, W ⊂ kn+1, and F : kn → kn+1 such that F¦v = ƒ and gdeg F = 1 < gdeg/ (gdeg h means the number of points in the generic fiber of h). Thus, in some sense, the result of this note improves our result in J. Pure Appl. Algebra 148 (2000) where it was shown that this phenomenon can occur when V ⊂ kn, W ⊂ km with m ≥ n + 2. In the case V, W ⊂ kn a similar example does not exist.
Słowa kluczowe
Wydawca
Rocznik
Tom
Strony
117--120
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
autor
- Instytut Matematyki, Uniwersytet Jagielloński, Reymonta 4, 30-059 Kraków, Poland, Marek.Karas@im.uj.edu.pl
Bibliografia
- [1] M. Artin, Algebraization of formal moduli: II. Existence of modifications, Ann. of Math. (2) 91 (1970), 88-135.
- [2] Z. Jelonek, The extension of regular and rational embeddings, Math. Ann. 277 (1987), 113-120.
- [3] M. Karaś, An estimate of the geometric degree of an extensions of some polynomial proper mappings, Univ. Iagel. Acta Math. 35 (1997), 131-135.
- [4] M. Karaś, Geometric degree of finite extension of projections, Univ. Iagel. Acta Math. 37 (1999), 109-119.
- [5] M. Karaś, Birational finite extensions, J. Pure Appl. Algebra 148 (2000), 251-253.
- [6] M. Karaś, Finite extensions of mappings from a smooth variety, Ann. Polon. Math. 75 (2000), 79-86.
- [7] M. Karaś, Finite extensions of mappings of finite sets, Bull. Polish Acad. Sci. Math. 50 (2002), 237-239.
- [8] M. Karaś, Geometric degree of finite extensions of mappings from a smooth variety, 3. Pure Appl. Algebra 212 (2008), 1145-1148.
- [9] M. Karaś, A note on geometric degree of finite extensions of mappings from a smooth variety, Bull. Polish Acad. Sci. Math. 56 (2008), 105-108.
- [10] M. Kwieciński, Extending finite mappings to affine space, J. Pure Appl. Algebra 76 (1991), 151-153.
- [11] S. Łojasiewicz, Introduction to Complex Analytic Geometry, PWN, Warszawa, 1988.
- [12] V. Srinivas, On the embedding dimension of the affine variety, Math. Ann. 289 (1991), 125-132.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0040-0015