Getzler relation and Virasoro conjecture for genus one

  • Yijie LinEmail author


We derive explicit universal equations for primary Gromov–Witten invariants by applying Getzler’s genus one relation to quantum powers of Euler vector field. As an application, we provide some evidences for the genus-1 Virasoro conjecture.


Getzler’s genus one relation Virasoro conjecture Quantum product Gromov–Witten invariants 

Mathematics Subject Classification




The author would like to thank Professor Xiaobo Liu for many helpful suggestions and Professor Jian Zhou for his encouragement.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Mathematics (Zhuhai)Sun Yat-Sen UniversityZhuhaiChina

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