We present a calculation that shows how the moduli of complex analytic elliptic
curves arises naturally from the Borel cohomology of an extended moduli space of
-bundles on a
torus. Furthermore, we show how the analogous calculation, applied to a moduli space of principal
bundles for a
central extension of
,
gives rise to Looijenga line bundles. We then speculate on the relation of
these calculations to the construction of complex analytic equivariant elliptic
cohomology.
