English

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.

Keywords

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