How to Calculate Homology Groups of Spaces of Nonsingular Algebraic Projective Hypersurfaces
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Solitons, geometry, and topology: on the crossroads, Tome 225 (1999), pp. 132-152
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A general method of computing cohomology groups of the space of nonsingular algebraic hypersurfaces of degree $d$ in $\mathbf{CP}^n$ is described. Using this method, rational cohomology groups of such spaces with $n=2$, $d\le 4$ and $n=3=d$ and also of the space of nondegenerate quadratic vector fields in $\mathbf C^3$ are calculated.
@article{TM_1999_225_a7,
author = {V. A. Vassiliev},
title = {How to {Calculate} {Homology} {Groups} of {Spaces} of {Nonsingular} {Algebraic} {Projective} {Hypersurfaces}},
journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
pages = {132--152},
publisher = {mathdoc},
volume = {225},
year = {1999},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TM_1999_225_a7/}
}
TY - JOUR AU - V. A. Vassiliev TI - How to Calculate Homology Groups of Spaces of Nonsingular Algebraic Projective Hypersurfaces JO - Trudy Matematicheskogo Instituta imeni V.A. Steklova PY - 1999 SP - 132 EP - 152 VL - 225 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TM_1999_225_a7/ LA - ru ID - TM_1999_225_a7 ER -
%0 Journal Article %A V. A. Vassiliev %T How to Calculate Homology Groups of Spaces of Nonsingular Algebraic Projective Hypersurfaces %J Trudy Matematicheskogo Instituta imeni V.A. Steklova %D 1999 %P 132-152 %V 225 %I mathdoc %U http://geodesic.mathdoc.fr/item/TM_1999_225_a7/ %G ru %F TM_1999_225_a7
V. A. Vassiliev. How to Calculate Homology Groups of Spaces of Nonsingular Algebraic Projective Hypersurfaces. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Solitons, geometry, and topology: on the crossroads, Tome 225 (1999), pp. 132-152. http://geodesic.mathdoc.fr/item/TM_1999_225_a7/