Tautological relations for stable maps to a target variety

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.

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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