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arXiv · 2610.17985

Cohomology ring of the strata of holomorphic differentials of genus 3

Prabhat Devkota·Myeongjae Lee
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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.

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Prabhat Devkota, Myeongjae Lee. 2026-10-13. Cohomology ring of the strata of holomorphic differentials of genus 3. https://arxiv.org/abs/2610.17985

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