Looijenga line bundles in complex analytic elliptic cohomology

Research output: Contribution to journalArticle

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 (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.
Original languageEnglish (US)
Pages (from-to)1-42
Number of pages42
JournalTunisian Journal of Mathematics
Volume2
Issue number1
DOIs
StatePublished - 2020

Fingerprint

Line Bundle
Cohomology
Moduli Space
Principal Bundle
Central Extension
Equivariant
Elliptic Curves
Bundle
Torus
Modulus

Cite this

Looijenga line bundles in complex analytic elliptic cohomology. / Rezk, Charles.

In: Tunisian Journal of Mathematics, Vol. 2, No. 1, 2020, p. 1-42.

Research output: Contribution to journalArticle

@article{d3b93e7b02e24eed87c1450bf8c67f33,
title = "Looijenga line bundles in complex analytic elliptic cohomology",
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 (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.",
author = "Charles Rezk",
year = "2020",
doi = "10.2140/tunis.2020.2.1",
language = "English (US)",
volume = "2",
pages = "1--42",
journal = "Tunisian Journal of Mathematics",
issn = "2576-7658",
number = "1",

}

TY - JOUR

T1 - Looijenga line bundles in complex analytic elliptic cohomology

AU - Rezk, Charles

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

U2 - 10.2140/tunis.2020.2.1

DO - 10.2140/tunis.2020.2.1

M3 - Article

VL - 2

SP - 1

EP - 42

JO - Tunisian Journal of Mathematics

JF - Tunisian Journal of Mathematics

SN - 2576-7658

IS - 1

ER -