Linear hyperelliptic Hodge integrals

Abstract

AbstractWe 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 $$\lambda $$ λ -class, and powers of a $$\psi $$ ψ -class pulled back along the branch map. This is achieved by using Atiyah–Bott localization on a stack of stable maps into the orbifold $$\left[ {\mathbb {P}}^1/{\mathbb {Z}}_2\right] $$ P 1 / Z 2 .