Check a polynomial map is finite

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Hi, I want to check the finiteness of a polynomial map of complex variables. In particular, I want to check whether the map $$f: \mathbb{C}^2 \to \mathbb{C}^2$$ $$f(x,y) = (x^3 - 3xy - 3x, y^3 - 3x^2 y +6y^2 +9y)$$ is finite ?