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

Time: Thu 2024-03-07 13.15 - 14.15

Location: Cramer room, Albano

Participating: Federico Cantero Moran (Universidad Autónoma de Madrid)

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).