Pseudostable Hodge integrals

TL;DR

This paper explores Hodge integrals on pseudostable curves, providing a comparison formula to relate them to stable curve integrals and analyzing their properties and implications for Gromov-Witten invariants.

Contribution

It introduces an explicit comparison formula for pseudostable Hodge integrals and investigates their relationship with stable integrals and Gromov-Witten invariants.

Findings

Pseudostable Hodge integrals equal stable ones when linear in lambda classes.

The equality does not hold for nonlinear lambda class integrals.

Pseudostable Gromov-Witten invariants match classical invariants for curves, but not for higher-dimensional targets.

Abstract

This paper initiates a study of Hodge integrals on moduli spaces of pseudostable curves. We prove an explicit comparison formula that allows one to effectively compute any pseudostable Hodge integral in terms of intersection numbers on moduli spaces of stable curves, and we use this comparison to prove that pseudostable Hodge integrals are equal to their stable counterparts when they are linear in lambda classes, but not when they are nonlinear. This suggests that pseudostable Gromov-Witten invariants are equal to usual Gromov-Witten invariants for target curves, but not for higher-dimensional target varieties.