Topological Order Complexes and Resolutions of Discriminant Sets
Publications de l'Institut Mathématique, _N_S_66 (1999) no. 80, p. 165
Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
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 topological
order complexes appear naturally in the conical resolutions of
many singular algebraic varieties, especially of discriminant
varieties, i.e. the spaces of singular geometric objects. These
resolutions generalize the simplicial resolutions to the case of
non-normal 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.
@article{PIM_1999_N_S_66_80_a9,
author = {V. A. Vassiliev},
title = {Topological {Order} {Complexes} and {Resolutions} of {Discriminant} {Sets}},
journal = {Publications de l'Institut Math\'ematique},
pages = {165 },
publisher = {mathdoc},
volume = {_N_S_66},
number = {80},
year = {1999},
zbl = {0953.55011},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_1999_N_S_66_80_a9/}
}
V. A. Vassiliev. Topological Order Complexes and Resolutions of Discriminant Sets. Publications de l'Institut Mathématique, _N_S_66 (1999) no. 80, p. 165 . http://geodesic.mathdoc.fr/item/PIM_1999_N_S_66_80_a9/