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For positive integers $d,m,n\geq 1$ with $(m,n)\not= (1,1)$ and $\Bbb K=\BbbR$ or $\Bbb C$, let $Q^{d,m}_{n}(\Bbb K)$ denote the space of $m$-tuples$(f_1(z),\cdots ,f_m(z))\in \Bbb K [z]^m$ of $\Bbb K$-coefficients monicpolynomials of the same degree $d$ such that polynomials $\{f_k(z)\}_{k=1}^m$have no common {\it real} root of multiplicity $\geq n$ (but may have complexcommon root of any multiplicity). %% These spaces can be regarded as one ofgeneralizations of the spaces defined and studied by Arnold and Vassiliev, andthey may be also considered as the real analogues of the spaces studied by B.Farb and J. Wolfson. In this paper, we shall determine their homotopy typesexplicitly and generalize some previously obtained results.

The homotopy type of spaces of real resultants with bounded multiplicity