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arXiv · 1603.02288

Meromorphic vector fields with single-valued solutions on complex surfaces

Adolfo Guillot
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Abstract

We study ordinary differential equations in the complex domain given by meromorphic vector fields on K\"ahler compact complex surfaces. We prove that if such an equation has a maximal single valued solution with Zariski-dense image (in particular, if it has an entire one) then, up to a bimeromorphic transformation, either the vector field is holomorphic or it preserves a fibration.

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Adolfo Guillot. 2016-03-07. Meromorphic vector fields with single-valued solutions on complex surfaces. https://doi.org/10.1016/j.aim.2019.106742

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