MEGA 2007Effective Methods in Algebraic Geometry Strobl, Austria, June 25th - 29th |
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Electronic Proceedings
Abstract
| Title | Iterated discriminants |
| Keywords | discriminant, generic point, cylindrical algebraic decomposition, CAD, singularities of discriminant hypersurface |
| Abstract | It is shown that the discriminant of a discriminant has the same irreducible factors as the product
of seven polynomials which are defined as the GCD of the generators of an elimination ideal. Under tame conditions of genericity, three of these polynomials are irreducible and generate the corresponding elimination ideal, while the four other are equal to one. Moreover the factors of two of these polynomials are factors of multiplicity at least two of the iterated discriminant and the factors of two others of the seven polynomials have multiplicity at least three. The proof involves an extended use of the notion of generic point of an algebraic variety and a careful study of the singularities of the hypersurface defined by a discriminant, which are interesting by them selves. |
The Institute is named after the famous Austrian mathematician Johann Radon (1887-1956)
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Juristische Person öffentlichen Rechts (BGBl 569/1921 idF BGBl I 130/2003)
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