Conformal blocks from vertex algebras and their connections on $\overline{\mathcal{M}}_{g,n}$

Chiara Damiolini; Angela Gibney; Nicola Tarasca

doi:10.2140/gt.2021.25.2235

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arXiv · 1901.06981

Conformal blocks from vertex algebras and their connections on $\overline{\mathcal{M}}_{g,n}$

Chiara Damiolini·Angela Gibney·Nicola Tarasca

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Abstract

We show that coinvariants of modules over vertex operator algebras give rise to quasi-coherent 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, Tsuchiya-Ueno-Yamada, and extend work of a number of researchers. 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. 2019-01-21. Conformal blocks from vertex algebras and their connections on $\overline{\mathcal{M}}_{g,n}$. https://doi.org/10.2140/gt.2021.25.2235

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