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