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arXiv · 2312.03355

Homological stability for the space of hypersurfaces with marked points

Alexis Aumonier·Ronno Das
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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.

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Alexis Aumonier, Ronno Das. 2023-12-06. Homological stability for the space of hypersurfaces with marked points. https://arxiv.org/abs/2312.03355

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