#### Vol. 2, No. 1, 2020

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Looijenga line bundles in complex analytic elliptic cohomology

### Charles Rezk

Vol. 2 (2020), No. 1, 1–42
##### Abstract

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 $U\phantom{\rule{0.3em}{0ex}}\left(1\right)$-bundles on a torus. Furthermore, we show how the analogous calculation, applied to a moduli space of principal bundles for a $K\left(ℤ,2\right)$ central extension of $U\phantom{\rule{0.3em}{0ex}}{\left(1\right)}^{d}$, gives rise to Looijenga line bundles. We then speculate on the relation of these calculations to the construction of complex analytic equivariant elliptic cohomology.

##### Keywords
elliptic cohomology, Looijenga line bundle
##### Mathematical Subject Classification 2010
Primary: 55N34
Secondary: 55N91, 55R40