Geodesic
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. 
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     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},
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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/