Looijenga line bundles in complex analytic elliptic cohomology

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

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Keywords

elliptic cohomology, Looijenga line bundle

Mathematical Subject Classification 2010

Primary: 55N34

Secondary: 55N91, 55R40

Milestones

Received: 26 February 2018

Revised: 4 August 2018

Accepted: 19 August 2018

Published: 22 March 2019

Authors

Charles Rezk
Department of Mathematics University of Illinois at Urbana-Champaign Urbana, IL 61801 United States

Vol. 2, No. 1, 2020

Charles Rezk

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors