Book contents
- Frontmatter
- Contents
- List of Contributors
- Preface
- 1 Birational Geometry of Algebraic Varieties and Shokurov’s Work
- 2 ACC for Log Canonical Thresholds for Complex Analytic Spaces
- 3 Conjectures on the Kodaira Dimension
- 4 Characterizing Terminal Fano Threefolds with the Smallest Anti-Canonical Volume, II
- 5 Uniform Rational Polytopes for Iitaka Dimensions
- 6 MMP for Algebraically Integrable Foliations
- 7 On Toric Fano Fibrations
- 8 Q-Fano Threefolds of Fano Index 13
- 9 Reflective Hyperbolic 2-Elementary Lattices, K3 Surfaces and Hyperkahler Manifolds
- 10 The Relative Du Bois Complex – on a Question of S. Zucker
- 11 Factorization Presentations
- 12 Spectrum Bounds in Geometry
- 13 On the DCC of Iitaka Volumes
- 14 Shokurov’s Index Conjecture for Quotient Singularities
- 15 A Note on the Sarkisov Program
- 16 Cluster Varieties and Toric Specializations of Fano Varieties
- 17 Birational Rigidity and Alpha Invariants of Fano Varieties
- 18 On F-Pure Inversion of Adjunction
- 19 On Termination of Flips and Fundamental Groups
- 20 Motivic Integration on Berkovich Spaces
11 - Factorization Presentations
Published online by Cambridge University Press: 06 December 2024
- Frontmatter
- Contents
- List of Contributors
- Preface
- 1 Birational Geometry of Algebraic Varieties and Shokurov’s Work
- 2 ACC for Log Canonical Thresholds for Complex Analytic Spaces
- 3 Conjectures on the Kodaira Dimension
- 4 Characterizing Terminal Fano Threefolds with the Smallest Anti-Canonical Volume, II
- 5 Uniform Rational Polytopes for Iitaka Dimensions
- 6 MMP for Algebraically Integrable Foliations
- 7 On Toric Fano Fibrations
- 8 Q-Fano Threefolds of Fano Index 13
- 9 Reflective Hyperbolic 2-Elementary Lattices, K3 Surfaces and Hyperkahler Manifolds
- 10 The Relative Du Bois Complex – on a Question of S. Zucker
- 11 Factorization Presentations
- 12 Spectrum Bounds in Geometry
- 13 On the DCC of Iitaka Volumes
- 14 Shokurov’s Index Conjecture for Quotient Singularities
- 15 A Note on the Sarkisov Program
- 16 Cluster Varieties and Toric Specializations of Fano Varieties
- 17 Birational Rigidity and Alpha Invariants of Fano Varieties
- 18 On F-Pure Inversion of Adjunction
- 19 On Termination of Flips and Fundamental Groups
- 20 Motivic Integration on Berkovich Spaces
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.
- Type
- Chapter
- Information
- Higher Dimensional Algebraic GeometryA Volume in Honor of V. V. Shokurov, pp. 163 - 191Publisher: Cambridge University PressPrint publication year: 2025