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1 results

  • 11 - Factorization Presentations

  • Edited by Christopher Hacon, University of Utah, Chenyang Xu, Princeton University, New Jersey
  • Book:
    Higher Dimensional Algebraic Geometry
    Published online:
    06 December 2024
    Print publication:
    02 January 2025, pp 163-191

  • Summary

    Modules over a vertex operator algebra V give rise to sheaves of coinvariants on moduli of stable pointed curves. If V satisfies finiteness and semisimplicity 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.