100 Adolfo Guillot

Adolfo Guillot (National Autonomous University of Mexico) // Meromorphic vector fields on algebraic surfaces having univalent solutions // Abstract: We consider algebraic, first-order, autonomous ordinary differential equations in two complex variables (meromorphic vector fields on compact algebraic surfaces, for instance, those coming from rational vector fields on affine surfaces), and discuss the very strong constraints imposed by the existence of one transcendental univalent solution: either there is some variable that integrates independently (the vector field preserves a fibration on the surface), or the surface is an abelian one and the vector field is linear.