Algebraic integrability of planar polynomial vector fields by extension to Hirzebruch surfaces

Carlos Galindo, Francisco Monserrat, Elvira Pérez-Callejo

We study algebraic integrability of complex planar polynomial vector fields $X=A(x,y)(\partial /\partial x)+B(x,y)(\partial /\partial y)$ through extensions to Hirzebruch surfac…