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

TL;DR

This paper computes the stable cohomology of the universal degree d hypersurface in projective space and provides a geometric interpretation of the stable classes, extending previous work by Tommasi and Das.

Contribution

It offers the first computation of the stable cohomology of the universal hypersurface and describes the geometric nature of the stable classes.

Findings

Stable cohomology groups are explicitly computed.

A geometric description of stable classes is provided.

The work extends prior results by Tommasi and Das.

Abstract

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 .