Algebraically constructible functions and signs of polynomials |
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Authors: | Adam Parusiński Zbigniew Szafraniec |
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Institution: | (1) Département de Mathématiques, Université d’Angers, 2 BD. Lavoisier, 49045 Angers Cedex, France;(2) School of Mathematics and Statistics, University of Sydney, 2006 Sydney, NSW, Australia;(3) Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland |
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Abstract: | LetW be a real algebraic set. We show that the following families of integer-valued functions onW coincide: (i) the functions of the formω →λ(X
ω
), where X
ω
are the fibres of a regular morphismf :X →W of real algebraic sets, (ii) the functions of the formω →χ(X
ω
), where X
ω
are the fibres of a proper regular morphismf :X →W of real algebraic sets, (iii) the finite sums of signs of polynomials onW. Such functions are called algebraically constructible onW. Using their characterization in terms of signs of polynomials we present new proofs of their basic functorial properties
with respect to the link operator and specialization.
Research partially supported by an Australian Research Council Small Grant. Second author also partially supported by KBN
610/P3/94. |
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Keywords: | 14P05 14P25 |
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