Pré-Publication, Document De Travail Année : 2023

Poincaré Duality, Degeneracy, and Real Lefschetz Property for T-Hypersurfaces

Résumé

In this article, we present two structural results about the Renaudineau-Shaw spectral sequence that computes the cohomology of T-hypersurfaces. The first is a Poincaré duality satisfied by all its pages of positive index. The second is a vanishing criterion. It reformulates the vanishing of the boundary operators of the spectral sequence as the injectivity of some morphisms induced in cohomology by the inclusion of the T-hypersurface in its surrounding toric variety. It implies that the Renaudineau-Shaw spectral sequence of a T-hypersurface degenerates at the second page if and only if the T-hypersurface satisfies a real version of the Lefschetz Hyperplane Section Theorem.

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Dates et versions

hal-04349997 , version 1 (18-12-2023)
hal-04349997 , version 2 (12-06-2025)
hal-04349997 , version 3 (21-10-2025)

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  • HAL Id : hal-04349997 , version 3

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Jules Chenal. Poincaré Duality, Degeneracy, and Real Lefschetz Property for T-Hypersurfaces. 2025. ⟨hal-04349997v3⟩
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