Conformal blocks from vertex algebras and their connections on ℳg,n

Damiolini, Chiara¹ ; Gibney, Angela² ; Tarasca, Nicola³

¹ Department of Mathematics, Princeton University, Princeton, NJ, United States, Department of Mathematics, Rutgers University, Piscataway, NJ, United States
² Department of Mathematics, Rutgers University, Piscataway, NJ, United States
³ Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA, United States

Geometry & topology, Tome 25 (2021) no. 5, pp. 2235-2286.

Résumé

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 $\mathcal{𝒟}$–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.

Détail

DOI : 10.2140/gt.2021.25.2235

Classification : 14C17, 14H10, 17B69, 16D90, 81R10, 81T40
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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