Betti numbers of stable map spaces to Grassmannians

TL;DR

This paper introduces a recursive method to compute Hodge and Betti numbers of moduli spaces of stable maps from genus 0 curves to Grassmannians, extending previous work on projective spaces.

Contribution

It generalizes existing techniques to Grassmannians, enabling systematic calculation of topological invariants for these moduli spaces.

Findings

Provides recursive formulas for Betti and Hodge numbers.

Extends methods from projective spaces to Grassmannians.

Facilitates computations for all degrees and marked points.

Abstract

Let $\bar{M}_{0,n}(G(r,V), d)$ be the coarse moduli space of stable degree $d$ maps from $n$-pointed genus $0$ curves to a Grassmann variety $G(r,V)$. We provide a recursive method for the computation of the Hodge numbers and the Betti numbers of $\bar{M}_{0,n}(G(r,V), d)$ for all $n$ and $d$. Our method is a generalization of Getzler and Pandharipande's work for maps to projective spaces.