# A remark on first integrals of vector fields

#### Preprint

We provide examples of vector fields on (C^3,0) admitting a formal first integral but no holomorphic first integral. These examples are related to a question raised by D. Cerveau and motivated by the celebrated theorems of Malgrange and Mattei-Moussu.

André da Silva

Martin Klimes

Julio Rebelo

### Publication

Year of publication: 2021