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When is a Distribution of Signs Locally Completable?

Published online by Cambridge University Press:  20 November 2018

F. Acquistapace ,
F. Broglia  and
E. Fortuna
F. Acquistapace
Affiliation:
Dipartimento di Matematica Université di Pisa Via F. Buonarroti 2 1-56127 Pisa Italy fax number: (39) 50 599524 e-mail: , broglia@dm.unipi.ite-mail: , fortuna@dm.unipi.it
F. Broglia
Affiliation:
Dipartimento di Matematica Université di Pisa Via F. Buonarroti 2 1-56127 Pisa Italy fax number: (39) 50 599524 e-mail: , broglia@dm.unipi.ite-mail: , fortuna@dm.unipi.it
E. Fortuna
Affiliation:
Dipartimento di Matematica Université di Pisa Via F. Buonarroti 2 1-56127 Pisa Italy fax number: (39) 50 599524 e-mail: , broglia@dm.unipi.ite-mail: , fortuna@dm.unipi.it
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Abstract

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Let V be an irreducible nonsingular algebraic surface, Y ⊂ V be an algebraic curve and P a point of Y. Suppose a sign distribution is given locally in a neighbourhood of P on some connected components of V — Y. We give an algorithmic criterion to decide whether this sign distribution is induced by a regular function or not. As an application, this criterion enables one to decide whether two semialgebraic sets can be locally separated or not.

Keywords

14P10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 3 , 01 June 1994 , pp. 449 - 473
Copyright
Copyright © Canadian Mathematical Society 1994

References

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