Seminario de Álgebra Conmutativa, Geometría Algebraica y Geometría Aritmética

Jueves 12 de junio a las 12:00h en el aula 420 del módulo 17 (Departamento de Matemáticas UAM)

Federico Cantero Morán

Título: On the cohomology of spaces of non-singular almost-complex hypersurfaces

Resumen: In 2023, Aumonier proved 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).