Publication:
Polynomial and regular images of R-n

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http://www.springerlink.com/content/0021-2172/
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Publication Date
2006
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Hebrew University Magnes Press
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Abstract
We obtain new necessary conditions for an n-dimensional semialgebraic subset of R-n to be a polynomial image of R-n. Moreover, we prove that a large family of planar bidimensional semialgebraic sets with piecewise linear boundary are images of polynomial or regular maps, and we estimate in both cases the dimension of their generic fibers.
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Geometria algebraica
Unesco subjects
1201.01 Geometría Algebraica
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J. Bochnak, M. Coste and M.-F. Roy, Gdomdtrie algdbrique rdelle, Ergebnisse der Mathematik 12, Springer-Verlag, Berlin-Heidelberg-New York, 1987. J. F. Fernando and J. M. Gamboa, Polynomial images ofR ~, Journal of Pure and Applied Algebra 179 (2003), 241-254. Z. Jelonek, A geometry of polynomial transformations of the real plane,Bulletin of the Polish Academy of Sciences. Mathematics 48 (2000), 57-62. Z. Jelonek, Geometry of real polynomial mappings, Mathematische Zeitschrift 239 (2002), 321-333. E. NSther, K6rper und Systeme rationaler Funktionen, Mathematische Annalen 76 (1915), 161-196. A. Schinzel, Selected Topics on Polynomials, The University of Michigan Press, Ann Arbor, 1982.
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https://hdl.handle.net/20.500.14352/49904
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