Linear Hyperelliptic Hodge Integrals

Published 16 Oct 2019 in math.AG | (1910.07330v1)

Abstract: We provide a closed form expression for linear Hodge integrals on the hyperelliptic locus. Specifically, we find a succinct combinatorial formula for all intersection numbers on the hyperelliptic locus with one $\lambda$-class, and powers of a $\psi$-class pulled back along the branch map. This is achieved by using Atiyah-Bott localization on a stack of stable maps into the orbifold $[\mathbb{P}^{1/\mathbb{Z}_2]$.}