We compute the equivariant cohomology of complex projective spaces associated to finite-dimensional representations C2, using ordinary graded on fundamental groupoid, with coefficients in Burnside ring Mackey functor. This extension RO(C2)-graded theory allows for definition Euler classes, which are used as generators spaces. As an application, we give version Bézout's theorem.

Quadratically parametrized smooth maps from one complex projective space to another are constructed as projections of the Segre map of the complexification. A classification theorem relates equivalence classes of projections to congruence classes of matrix pencils. Maps from the 2-sphere to the complex projective plane, which generalize stereographic projection, and immersions of the complex pr...

We consider the vanishing problem for higher cohomology groups on certain infinite-dimensional complex spaces: good branched coverings of suitable projective spaces and subvarieties with a finite free resolution in a projective space P(V ) (e.g. complete intersections or cones over finitedimensional projective spaces). In the former case we obtain the vanishing result for H. In the latter case ...