Volume 25, issue 5 (2021)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 25
Issue 5, 2167–2711
Issue 4, 1631–2166
Issue 3, 1087–1630
Issue 2, 547–1085
Issue 1, 1–546

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Conformal blocks from vertex algebras and their connections on $\overline{\mathcal{M}}_{g,n}$

Chiara Damiolini, Angela Gibney and Nicola Tarasca

Geometry & Topology 25 (2021) 2235–2286
Abstract

We show that coinvariants of modules over vertex operator algebras give rise to quasicoherent sheaves on moduli of stable pointed curves. These generalize Verlinde bundles or vector bundles of conformal blocks defined using affine Lie algebras studied first by Tsuchiya, Kanie, Ueno and Yamada, and extend work of others. The sheaves carry a twisted logarithmic 𝒟–module structure, and hence support a projectively flat connection. We identify the logarithmic Atiyah algebra acting on them, generalizing work of Tsuchimoto for affine Lie algebras.

Keywords
vertex algebras, conformal blocks and coinvariants, connections and Atiyah algebras, sheaves on moduli of curves, Chern classes of vector bundles on moduli of curves
Mathematical Subject Classification 2010
Primary: 14C17, 14H10, 17B69
Secondary: 16D90, 81R10, 81T40
References
Publication
Received: 5 March 2019
Revised: 19 April 2020
Accepted: 2 October 2020
Published: 3 September 2021
Proposed: Lothar Göttsche
Seconded: Dan Abramovich, Jim Bryan
Authors
Chiara Damiolini
Department of Mathematics
Princeton University
Princeton, NJ
United States
Department of Mathematics
Rutgers University
Piscataway, NJ
United States
Angela Gibney
Department of Mathematics
Rutgers University
Piscataway, NJ
United States
Nicola Tarasca
Department of Mathematics and Applied Mathematics
Virginia Commonwealth University
Richmond, VA
United States