On global generation of vector bundles on the moduli space of curves from representations of vertex operator algebras

TL;DR

This paper investigates the conditions under which sheaves of coinvariants derived from vertex operator algebras are globally generated on the moduli space of curves, extending previous results and providing new examples and evidence.

Contribution

It extends known results on global generation for affine VOAs to broader classes of vertex operator algebras and explores cases where global generation does not hold.

Findings

Global generation holds for certain VOAs on the moduli space of curves.

Examples where global generation fails are identified.

Additional evidence suggests positivity properties of these sheaves.

Abstract

We consider global generation of sheaves of coinvariants on the moduli space of curves given by simple modules over certain vertex operator algebras, extending results for affine VOAs at integrable levels on stable pointed rational curves. Examples where global generation fails, and further evidence of positivity are given.