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Conformal blocks from
vertex algebras and their connections on
$\overline{\mathcal{M}}_{g,n}$
Chiara Damiolini, Angela Gibney and Nicola Tarasca |
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Geometry & Topology 25 (2021) 2235–2286
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Abstract |
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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 –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
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Mathematical Subject Classification 2010
Primary: 14C17, 14H10, 17B69
Secondary: 16D90, 81R10, 81T40
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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
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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 |
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| Nicola Tarasca | |
| Department of Mathematics and
Applied Mathematics Virginia Commonwealth University Richmond, VA United States |
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