Meromorphic vector fields with single-valued solutions on complex surfaces

摘要

We study ordinary differential equations in the complex domain given by meromorphic vector fields on compact complex Kahler surfaces. We prove that if such an equation has a maximal single-valued solution (in particular, an entire one) whose image is not contained in a proper analytic subset then, up to a bimeromorphic transformation, either the vector field is holomorphic or it preserves a fibration. (C) 2019 Elsevier Inc. All rights reserved.