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Conformal blocks for modular vertex algebras
Abstract
Given a vertex operator algebra V over ℂ, it is known how to define so-called sheaves of coinvariants and conformal blocks on the moduli space ℳ̅g,n of stable, n-pointed, genus g curves. We extend this theory to vertex algebras equipped with a notion of change of coordinates over any algebraically closed field. As a by-product of our arguments, we also show that a number of standard assumptions in these constructions can be removed, such as being C1-cofinite or CFT-type.
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BibTeX
@misc{griffin2026conformal,
title = {{Conformal blocks for modular vertex algebras}},
author = {Colton Griffin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38376},
eprint = {2609.38376},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38376},
}
RIS
TY - UNPB
TI - Conformal blocks for modular vertex algebras
AU - Colton Griffin
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38376
UR - https://arxiv.org/abs/2609.38376
AB - Given a vertex operator algebra V over ℂ, it is known how to define so-called sheaves of coinvariants and conformal blocks on the moduli space ℳ̅_g,n of stable, n-pointed, genus g curves. We extend this theory to vertex algebras equipped with a notion of change of coordinates over any algebraically closed field. As a by-product of our arguments, we also show that a number of standard assumptions in these constructions can be removed, such as being C_1-cofinite or CFT-type.
ER -