Factorization presentations
Algebraic Geometry
2022-08-12 v2 Representation Theory
Abstract
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 bundles. This relies on factorization, an isomorphism of spaces of coinvariants at a nodal curve with a finite sum of analogous spaces on the normalization of the curve. Here we introduce the notion of a factorization presentation, and using this, we show that finiteness conditions on V imply the sheaves of coinvariants are coherent on moduli spaces of pointed stable curves without any assumption of semisimplicity.
Cite
@article{arxiv.2207.05110,
title = {Factorization presentations},
author = {Chiara Damiolini and Angela Gibney and Daniel Krashen},
journal= {arXiv preprint arXiv:2207.05110},
year = {2022}
}