Homological stability for the space of hypersurfaces with marked points
Algebraic Topology
2023-12-07 v1 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.2312.03355,
title = {Homological stability for the space of hypersurfaces with marked points},
author = {Alexis Aumonier and Ronno Das},
journal= {arXiv preprint arXiv:2312.03355},
year = {2023}
}
Comments
42 pages; comments welcome!