Stable cohomology of the universal degree $d$ hypersurface in $\mathbb{P}^n

Algebr. Geom. Topol. 23 (2023) 3071-3088 Let $U_{d,n}^*$ be the universal degree $d$ hypersurface in $\mathbb{P}^n$. In this paper we compute the stable (with respect to $d$) cohomology of $U_{d,n}^*$ and give a geometric description of the stable classes. This builds on work of Tommasi and Das .