2023/12/06 by Alexis Aumonier, Aumonier, Alexis, Ronno Das +1
Mathematics · #14J70 #55R80 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2312.03355
openalex publication_date 2023/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the space of smooth marked hypersurfaces in a given linear system. Specifically, we prove a homology h-principle to compare it with a space of sections of an appropriate jet bundle. Using rational models, we compute its rational cohomology in a range of degrees, and deduce a homological stability result for hypersurfaces of increasing degree. We also describe the Hodge weights on the stable cohomology, and thereby connect our topological result to motivic results of Howe.