Arkiv för Matematik

Volume 58 (2020)

Number 1

Tautological relations for stable maps to a target variety

Pages: 19 – 38



Younghan Bae (Department of Mathematics, ETH Zürich, Switzerland)


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 [20], we construct non-trivial tautological relations parallel to Pixton’s double ramification cycle relations for the moduli of curves. Examples and applications are discussed.

2010 Mathematics Subject Classification

Primary 14H10. Secondary 14N35.

The author was supported in part by ERC Grant ERC-2017-AdG-786580-MACI and Korea Foundation for Advanced Studies.

Received 30 April 2019

Received revised 30 August 2019

Accepted 20 September 2019

Published 21 July 2022