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Article

Homology of Spaces of Non-Resultant Homogeneous Polynomial Systems in R^2 and C^2

Arnold Mathematical Journal. 2015. Vol. 1. No. 3. P. 233-242.

The resultant variety in the space of systems of homogeneous polynomials of some given degrees consists of such systems having non-trivial solutions. We calculate the integer cohomology groups of all spaces of non-resultant systems of polynomials R2→R, and also the rational cohomology rings of spaces of non-resultant systems and non-m-discriminant polynomials in C2.