# On factorization and vector bundles of conformal blocks from vertex algebras

@article{Damiolini2019OnFA, title={On factorization and vector bundles of conformal blocks from vertex algebras}, author={Chiara Damiolini and A. Gibney and Nicola Tarasca}, journal={arXiv: Algebraic Geometry}, year={2019} }

Modules over conformal vertex algebras give rise to sheaves of coinvariants and conformal blocks on moduli of stable pointed curves. Here we prove the factorization conjecture for these sheaves. Our results apply in arbitrary genus and for a large class of vertex algebras. As an application, sheaves defined by finitely generated admissible modules over vertex algebras satisfying natural hypotheses are shown to be vector bundles. Factorization is essential to a recursive formulation of…

## 9 Citations

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

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We show that coinvariants of modules over conformal vertex algebras give rise to quasi-coherent sheaves on moduli of stable pointed curves. These generalize Verlinde bundles or vector bundles of…

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Representations of certain vertex algebras, here called of CohFT-type, can be used to construct vector bundles of coinvariants and conformal blocks on moduli spaces of stable curves [DGT2]. We show…

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We associate to any holomorphic vertex algebra a collection of Teichm\"{u}ller modular forms, one in each genus. In genus one we obtain the character of the vertex algebra, and we thus reprove Zhu's…

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In recent work, Damiolini-Gibney-Tarasca showed that for a $C_2$-cofinite rational CFT-type vertex operator algebra $\mathbb V$, sheaves of conformal blocks are locally free and satisfy the…

### Genus-zero Permutation-twisted Conformal Blocks for Tensor Product Vertex Operator Algebras: The Tensor-factorizable Case

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Let V “ À n P N V p n q be a vertex operator algebra (VOA), let E be a ﬁnite set, and let G be a subgroup of the permutation group Perm p E q which acts on V b E in a natural way. For each g P G ,…

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Propagation is a standard way of producing new conformal blocks from old ones that corresponds to the geometric procedure of adding new distinct points to a pointed compact Riemann surface. On the…

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We show that coinvariants of modules over conformal vertex algebras give rise to quasi-coherent sheaves on moduli of stable pointed curves. These generalize Verlinde bundles or vector bundles of…

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Representations of certain vertex algebras, here called of CohFT-type, can be used to construct vector bundles of coinvariants and conformal blocks on moduli spaces of stable curves [DGT2]. We show…

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