# Tautological relations for stable maps to a target variety

## TL;DR

This paper introduces tautological relations for the moduli space of stable maps to a target variety, extending known relations for curves and providing new tools for understanding their geometry.

## Contribution

It constructs new tautological relations for stable maps using the double ramification cycle formula, expanding the framework beyond curves.

## Key findings

- New tautological relations for stable maps are established.
- Examples demonstrate the applicability of these relations.
- Potential applications in enumerative geometry are discussed.

## Abstract

We define tautological relations for the moduli space of stable maps to a target variety. Using the double ramification cycle formula for target varieties of Janda-Pandharipande-Pixton-Zvonkine, we construct nontrivial tautological relations parallel to Pixton's double ramification cycle relations for the moduli of curves. Examples and applications are discussed.