Year: 2026
Type: preprint
Abstract: We prove that the rational Chow ring of every connected component of the multi-scale compactifications of the genus three strata $\mathcal{H}(4), \mathcal{H}(2,2)$ and $\mathcal{H}(3,1)$ is generated by boundary-stratum classes. Our proof shows Chow-Künneth generation property of boundary strata of the multi-scale compactification by reducing the boundary analysis to lower-genus generalized strata of meromorphic differentials, including residueless loci, described through plane-quartic and plane-cubic models. As a consequence, the rational cycle-class map is an isomorphism and the compactifications have no odd rational cohomology.
Source: arXiv (Cornell University)
Authors: Devkota, Prabhat, Lee, Myeongjae
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221816588