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Regular version of the site

Article

Real cohomology groups of the space of nonsingular curves of degree 5 in ${\mathbb C}P^2$

Annales de la Faculté des Sciences de Toulouse. 2005. Vol. 14. No. 3. P. 395-434.
We give a modification of V. A. Vassiliev’s method of calculating cohomology groups of spaces of nonsingular projective complex hypersufaces. Our construction is less “canonical” than V. A. Vassiliev’s one, but in some cases it allows to simplify the calculations. We apply our method to prove that the Poincar´e polynomial of the space of homogeneous polynomials that define nonsingular quintics in $\mathbb{C}P^2$ is equal to $(1 + t)(1 + t^3)(1 + t^5)$.