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Continuity Loci for Polynomial Systems

In: Algebra, Arithmetic and Geometry with Applications

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  • André Galligo
  • Michał Kwieciński

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.

Suggested Citation

  • André Galligo & Michał Kwieciński, 2004. "Continuity Loci for Polynomial Systems," Springer Books, in: Chris Christensen & Avinash Sathaye & Ganesh Sundaram & Chandrajit Bajaj (ed.), Algebra, Arithmetic and Geometry with Applications, pages 315-324, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18487-1_20
    DOI: 10.1007/978-3-642-18487-1_20
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