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math.AG2025
Real Toric Varieties: Interactions between their Geometry and their Topology
Jules Chenal, Matilde Manzaroli
In the present article, we investigate the topology of real toric varieties, especially those whose torus is not split over the field of real numbers. We describe some canonical fi…
math.AG2024
On the First Page of the Renaudineau-Shaw Spectral Sequence
Jules Chenal
In this article, we study the topology of T-hypersurfaces. These cellular hypersurfaces are generalisations of the cellular complexes used to describe the real loci of varieties ob…
math.AG2023
Poincaré Duality, Degeneracy, and Real Lefschetz Property for T-Hypersurfaces
Jules Chenal
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 sat…