Continuity Loci for Polynomial Systems

André Galligo and Michał Kwieciński

A chapter in Algebra, Arithmetic and Geometry with Applications, 2004, pp 315-324 from Springer

Abstract: Abstract We consider the topology induced by Hausdorff distance on the projective subvarieties of P m(C), the projective complex space of dimension m. We construct the minimal stratification, for this topology, of the space of coefficients of a homogeneous polynomial system with parameters. We give an algorithmic description of this stratification based on some usual algorithms in computer algebra such as equidimensional decomposition or normalization of a projective variety and also on a not so usual one, the fiber power of a morphism. The input algorithmic problem is an algebraic question in Q all the coefficients of the intermediate polynomials that we will consider are algebraic numbers. Our methods of proof of theorems, however, rely on analytic geometric properties.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18487-1_20

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DOI: 10.1007/978-3-642-18487-1_20

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