On some hyperelliptic Hurwitz–Hodge integrals

Abstract We address Hodge integrals over the hyperelliptic locus. Recently Afandi computed, via localisation techniques, such one-descendant and showed that they are Stirling numbers. give another proof of same statement by a very short argument, exploiting Chern classes spin structures relations arising from Topological Recursion in sense Eynard Orantin. These techniques seem also suitable to deal with three orthogonal generalisations: (1) extension r -hyperelliptic locus; (2) an arbitrary number non-Weierstrass pairs points; (3) multiple descendants.