Poincar{\'e} Duality, Degeneracy, and Real Lefschetz Property for T-Hypersurfaces
Algebraic Geometry
2025-10-23 v3 Algebraic Topology
Abstract
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 Poincar{\'e} 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.
Keywords
Cite
@article{arxiv.2312.11919,
title = {Poincar{\'e} Duality, Degeneracy, and Real Lefschetz Property for T-Hypersurfaces},
author = {Jules Chenal},
journal= {arXiv preprint arXiv:2312.11919},
year = {2025}
}