• Corpus ID: 202558729

# 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}
}
• Published 10 September 2019
• Mathematics
• arXiv: Algebraic Geometry
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…
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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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