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2021 Conformal blocks from vertex algebras and their connections on M ¯ g , n
Chiara Damiolini, Angela Gibney, Nicola Tarasca
Geom. Topol. 25(5): 2235-2286 (2021). DOI: 10.2140/gt.2021.25.2235

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.

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Chiara Damiolini. Angela Gibney. Nicola Tarasca. "Conformal blocks from vertex algebras and their connections on M ¯ g , n ." Geom. Topol. 25 (5) 2235 - 2286, 2021. https://doi.org/10.2140/gt.2021.25.2235

Information

Received: 5 March 2019; Revised: 19 April 2020; Accepted: 2 October 2020; Published: 2021
First available in Project Euclid: 12 October 2021

Digital Object Identifier: 10.2140/gt.2021.25.2235

Subjects:
Primary: 14C17, 14H10, 17B69
Secondary: 16D90, 81R10, 81T40

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.25 • No. 5 • 2021
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