Let $M_{I}$ be a hyperkähler manifold with $f:M_{I}\rightarrow N$ a complex torus fibration, along with a section $s:N\rightarrow M_{I}$ and an ample line bundle $\mathcal{L}$ with first Chern class represented by a hyperkähler metric $\omega_{I}$. We assume further the induced polarization on the smooth fibers of $f$ is principal and that $N$ is projective.