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

TL;DR

This paper proves that the monodromy group of a specific polynomial's Picard-Fuchs equation is the symplectic group, correcting previous misconceptions about its structure.

Contribution

It establishes the irreducibility of the Picard-Fuchs equation's monodromy group for the given polynomial, clarifying its algebraic properties.

Findings

The monodromy group is the symplectic group Sp(4,C).

Previous results about the monodromy representation were incorrect.

The Zariski closure of the monodromy group is explicitly identified.

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.