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arXiv · 2207.05110

Factorization presentations

Chiara Damiolini·Angela Gibney·Daniel Krashen
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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.

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Chiara Damiolini, Angela Gibney, Daniel Krashen. 2022-07-11. Factorization presentations. https://arxiv.org/abs/2207.05110

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