# Vertex algebras of CohFT-type

@article{Damiolini2019VertexAO, title={Vertex algebras of CohFT-type}, author={Chiara Damiolini and Angela Gibney and Nicola Tarasca}, journal={arXiv: Algebraic Geometry}, year={2019} }

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 that such bundles define semisimple cohomological field theories. As an application, we give an expression for their total Chern character in terms of the fusion rules, following the approach and computation in [MOPPZ] for bundles given by integrable modules over affine Lie algebras. It follows that…

## 7 Citations

On factorization and vector bundles of conformal blocks from vertex algebras

- Mathematics
- 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…

Conformal blocks from vertex algebras and their
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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…

Unbounded field operators in categorical extensions of conformal nets

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We prove the equivalence of VOA tensor categories and conformal net tensor categories for the following examples: all WZW models; all lattice VOAs; all unitary parafermion VOAs; type $ADE$ discrete…

Convergence of Sewing Conformal Blocks

- Mathematics
- 2020

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…

On global generation of vector bundles on the moduli space of curves from representations of vertex operator algebras

- Mathematics
- 2021

We consider global generation of sheaves of coinvariants on the moduli space of curves given by simple modules over certain vertex operator algebras, extending results for affine VOAs at integrable…

Factorization Resolutions

- Mathematics
- 2022

. Modules over a vertex operator algebra V give rise to sheaves of coinvariants on moduli of stable pointed curves. If V satisﬁes ﬁniteness and semi-simplicity conditions, these sheaves are vector…

Lazy tournaments and multidegrees of a projective embedding of $\overline{M}_{0,n}$

- Mathematics
- 2021

We provide a new geometric interpretation of the multidegrees of the (iterated) Kapranov embedding Φn : M0,n+3 ↪→ P×P×· · ·×P, where M0,n+3 is the moduli space of stable genus 0 curves with n + 3…

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