Year: 2026
Type: preprint
Abstract: We consider the moduli stack $\mathcal{H}_{g,d}$ parametrising maps $θ\colon C\to L$ of degree $d$ between complex curves of genera $g$ and $0$. We provide a splitting of the stable rational cohomology of $\mathcal{H}_{g,d}$, for $g\to\infty$, in terms of degrees of intermediate covers, and identify each direct summand in terms of factorisation homology. For $2\le d\le 5$, 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 $d=4,5$.
Source: arXiv (Cornell University)
Author: Bianchi, Andrea
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214990986