Poincar\'e polynomials of stable map spaces to Grassmannians

TL;DR

This paper derives generating functions for Betti numbers of moduli spaces of genus zero stable maps to Grassmannians for degrees 2 and 3, advancing understanding of their topological structure.

Contribution

It provides explicit generating functions for Betti numbers of these moduli spaces for degrees 2 and 3, a novel contribution to algebraic geometry.

Findings

Betti number generating functions for degree 2 and 3 maps

Enhanced understanding of the topology of stable map spaces

Explicit formulas for specific degrees

Abstract

In this paper, we give generating functions for the Betti numbers of $\bar{M}_{0,0}({G}(k,n),d)$, the moduli stack of zero pointed genus zero degree $d$ stable maps to the Grassmannian ${G}(k,n)$ for $d=2$ and 3.