### A compactification of ${\left({\u2102}^{*}\right)}^{4}$ with no non-constant meromorphic functions

For each 2-dimensional complex torus $T$, we construct a compact complex manifold $X\left(T\right)$ with a ${\u2102}^{2}$-action, which compactifies ${\left({\u2102}^{*}\right)}^{4}$ such that the quotient of ${\left({\u2102}^{*}\right)}^{4}$ by the ${\u2102}^{2}$-action is biholomorphic to $T$. For a general $T$, we show that $X\left(T\right)$ has no non-constant meromorphic functions.