PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 66(80), pp. 165187 (1999) 

Topological order complexes and resolutions of discriminant setsV. A. VassilievSteklov Math. Inst., Gubkina 8, 117966 Moscow and Independent Moscow University, Moscow, RussiaAbstract: If elements of a partially ordered set run over a topological space, then the corresponding order complex admits a natural topology, providing that similar interior points of simplices with close vertices are close to one another. Such {\it topological order complexes} appear naturally in the {\it conical resolutions} of many singular algebraic varieties, especially of {\it discriminant varieties}, i.e. the spaces of singular geometric objects. These resolutions generalize the {\it simplicial resolutions} to the case of nonnormal varieties. Using these order complexes we study the cohomology rings of many spaces of nonsingular geometrical objects, including the spaces of nondegenerate linear operators in $R^n$, $C^n$ or $H^n$, of homogeneous functions $R^2 \to R^1$ without roots of high multiplicity in $RP^1$, of nonsingular hypersurfaces of a fixed degree in $CP^n$, and of Hermitian matrices with simple spectra. Classification (MSC2000): 14J17; 55U99 Full text of the article:
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