Looijenga line bundles in complex analytic elliptic cohomology

Abstract

We present a calculation, which shows how the moduli of complex analytic elliptic curves arises naturally from the Borel cohomology of an extended moduli space of $U(1)$-bundles on a torus. Furthermore, we show how the analogous calculation, applied to a moduli space of principal bundles for a $K(\mathbb{Z},2)$ central extension of $U(1{)}^d$ give rise to Looijenga line bundles. We then speculate on the relation of these calculations to the construction of complex analytic equivariant elliptic cohomology.

Results are unchanged from previous version. However, exposition has been rewritten to be more friendly (and a few points added), and proofs have been streamlined somewhat. 29 pages

References in corpus (1)

• Categorical Tori

Cited by in corpus (1)

• Equivariant Elliptic Cohomology and Mapping Stacks