Homology of Spaces of Non-Resultant Homogeneous Polynomial Systems in $${\mathbb R}^2$$ and $${\mathbb C}^2$$
Tóm tắt
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
$${\mathbb R}^2 \rightarrow {\mathbb R}$$
, and also the rational cohomology rings of spaces of non-resultant systems and non-m-discriminant polynomials in
$${\mathbb C}^2$$
.
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