We show that in the category of complex algebraic varieties, the Eilenberg–Moore spectral sequence can be endowed with a weight filtration. This implies that it degenerates if all spaces involved have pure cohomology. As application, we compute the rational cohomology of an algebraic $G$-variety $X$ ($G$ being a connected algebraic group) in terms of its equivariant cohomology provided that $H_G^{*}\left(X\right)$ is pure. This is the case, for example, if $X$ is smooth and has only finitely many orbits. We work in the category...

The integral representation for the multiplicity of an isolated zero of a holomorphic mapping $f:({ℂ}^n,0)\to ({ℂ}^n,0)$ by means of Weil’s formulae is obtained.

Given adjacent subanalytic strata $(X,Y)$ in ${\mathbf{R}}^n$ verifying Kuo’s ratio test $\left(r\right)$ (resp. Verdier’s $\left(w\right)$-regularity) we find an open dense subset of the codimension $k$$C^1$ submanifolds $W$ (wings) containing $Y$ such that $(X\cap W,Y)$ is generically Whitney $\left(b^{\pi }\right)$-regular is exactly one more than the dimension...