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Cohomology ring of the strata of holomorphic differentials of genus 3
Abstract
We prove that the rational Chow ring of every connected component of the multi-scale compactifications of the genus three strata ℋ(4), ℋ(2,2) and 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.
Related
- Semipositivity and complete subvarieties of projectivised strata of holomorphic differentials
- Asymptotics of Masur-Veech volume of strata of quadratic differentials with many simple poles
- Euler characteristics of strata of k-differentials
- The determinant of the Dirichlet-to-Neumann map for a surface with boundary and periods of holomorphic differentials on its double
- Gauss-Manin Connection in Disguise: Holomorphic Anomaly Equations and Higher Genus Real Gromov-Witten Invariants
BibTeX
@misc{devkota2026cohomology,
title = {{Cohomology ring of the strata of holomorphic differentials of genus 3}},
author = {Prabhat Devkota and Myeongjae Lee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17985},
eprint = {2610.17985},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17985},
}
RIS
TY - UNPB
TI - Cohomology ring of the strata of holomorphic differentials of genus 3
AU - Prabhat Devkota
AU - Myeongjae Lee
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17985
UR - https://arxiv.org/abs/2610.17985
AB - We prove that the rational Chow ring of every connected component of the multi-scale compactifications of the genus three strata ℋ(4), ℋ(2,2) and 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.
ER -