Relations for quadratic Hodge integrals via stable maps

TL;DR

This paper uses virtual localization on the moduli space of stable maps to derive relations between quadratic Hodge integrals, showing certain generating series are polynomial, advancing understanding of these geometric invariants.

Contribution

It introduces new relations for quadratic Hodge integrals using virtual localization, and proves polynomiality of specific generating series.

Findings

Derived new relations between Hodge integrals

Proved polynomiality of generating series

Enhanced computational techniques for stable maps

Abstract

Following Faber-Pandharipande, we use the virtual localization formula for the moduli space of stable maps to $ \mathbb{P}^1 $ to compute relations between Hodge integrals. We prove that certain generating series of these integrals are polynomials.