PreprintCC BY 4.0arXiv
Stable rational cohomology splitting of moduli of branched covers of curves
Abstract
We consider the moduli stack ℋg,d parametrising maps θ: C→ L of degree d between complex curves of genera g and $0$. We provide a splitting of the stable rational cohomology of ℋg,d, for g→∞, in terms of degrees of intermediate covers, and identify each direct summand in terms of factorisation homology. For 2≤ d≤ 5, we further interpret the stable rational cohomology in terms of configuration spaces with labels in partial abelian monoids; we show in particular the existence of stable odd-dimensional cohomology classes for d=4,5.
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BibTeX
@misc{bianchi2026stable,
title = {{Stable rational cohomology splitting of moduli of branched covers of curves}},
author = {Andrea Bianchi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36884},
eprint = {2609.36884},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36884},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Stable rational cohomology splitting of moduli of branched covers of curves
AU - Andrea Bianchi
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.36884
UR - https://arxiv.org/abs/2609.36884
AB - We consider the moduli stack ℋ_g,d parametrising maps θ: C→ L of degree d between complex curves of genera g and $0$. We provide a splitting of the stable rational cohomology of ℋ_g,d, for g→∞, in terms of degrees of intermediate covers, and identify each direct summand in terms of factorisation homology. For 2≤ d≤ 5, we further interpret the stable rational cohomology in terms of configuration spaces with labels in partial abelian monoids; we show in particular the existence of stable odd-dimensional cohomology classes for d=4,5.
ER -