Authors: Jules Chenal ^1,2,3,4

• 1 Université de Lille
• 2 Laboratoire Paul Painlevé
• 3 Laboratoire Paul Painlevé - UMR 8524 [LPP]
• 4 Universitetet i Oslo

In this article, we present two structural results about the Renaudineau–Shaw spectralsequence 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.

• 14P25 - Topology of real algebraic varieties
• 14T90 - Applications of tropical geometry