On the scanning map and the space of smooth projective hypersurfaces

Ángel Javier Alonso; Federico Cantero-Morán

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arXiv · 2312.03939

On the scanning map and the space of smooth projective hypersurfaces

Ángel Javier Alonso·Federico Cantero-Morán

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Abstract

The space of degree d smooth projective hypersurfaces of CP n admits a scanning map to a certain space of sections. We compute a rational homotopy model of the action by conjugation of the group U (n + 1) on this space of sections, from which we deduce that the scanning map induces a monomorphism on cohomology when d > 2. Our main technique is the rational homotopy theory of Sullivan and, more specifically, a Sullivan model for the action by conjugation of a connected topological group on a space of sections.

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BibTeX RIS

Ángel Javier Alonso, Federico Cantero-Morán. 2023-12-06. On the scanning map and the space of smooth projective hypersurfaces. https://arxiv.org/abs/2312.03939

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