Intersections of $\psi$ classes on Hassett Spaces for genus $0$ with all weights $\frac{1}{2}$

TL;DR

This paper derives a closed-form formula for intersections of psi-classes on genus 0 Hassett spaces with equal weights of 1/2, connecting intersection theory with generating functions and the Witten-potential.

Contribution

It introduces a novel closed formula for psi-class intersections on these Hassett spaces and links it to generating functions derived from the Witten-potential.

Findings

Derived a closed formula for psi-class intersections.

Connected intersection theory with generating functions.

Provided a new computational tool for Hassett spaces.

Abstract

Hassett spaces are moduli spaces of weighted stable pointed curves. In this work, we consider such spaces of curves of genus $0$ with weights all $\frac{1}{2}$. These spaces are interesting as they are isomorphic to $\overline{M}_{0,n}$ but have different universal families and different intersection theory. We develop a closed formula for intersections of $\psi$-classes on such spaces. In our main result, we encode the formula for top intersections in a generating function obtained by applying a differential operator to the Witten-potential.