On factorization and vector bundles of conformal blocks from vertex algebras
Algebraic Geometry
2023-12-25 v5 Quantum Algebra
Abstract
Representations of vertex operator algebras define sheaves of coinvariants and conformal blocks on moduli of stable pointed curves. Assuming certain finiteness and semisimplicity conditions, we prove that such sheaves satisfy the factorization conjecture and consequently are vector bundles. Factorization is essential to a recursive formulation of invariants, like ranks and Chern classes, and to produce new constructions of rational conformal field theories and cohomological field theories.
Cite
@article{arxiv.1909.04683,
title = {On factorization and vector bundles of conformal blocks from vertex algebras},
author = {Chiara Damiolini and Angela Gibney and Nicola Tarasca},
journal= {arXiv preprint arXiv:1909.04683},
year = {2023}
}
Comments
55 pages. Final version, to appear in the Annales scientifiques de l'\'Ecole normale sup\'erieure