Irreducibility of the Picard-Fuchs equation related to the Lotka-Volterra polynomial $ x^2 y^2(1-x-y) $

Abstract

We prove that the Zarisky closure of the monodromy group of the polynomial $ x^2 y^2(1-x-y) $ is the symplectic group $Sp(4,\mathbb C)$. This shows that some previous results about this monodromy representation are wrong.