Federico Cantero Moran: On the cohomology of spaces of non-singular almost-complex hypersurfaces

Abstract.

Recently Aumonier has proven that the scanning map from the space of non-singular hypersurfaces in a smooth projective complex variety \(V\) to a certain space of sections induces an integral homology isomorphism in a range of degrees. In this talk we will show that when \(V\) is the complex projective space, the scanning map induces a monomorphism in rational homology in all degrees. This recovers a result of Peters and Steenbrink that finds a copy of the rational homology of the projective general linear group inside the rational homology of the space of projective non-singular hypersurfaces. The main tool in the proof is a Borel construction on the rational homotopy models of section spaces. This is a joint work with Ángel Alonso (U. Graz).