Modules and generalizations of Joyce vertex algebras

2025/05/30 by Bu, Chenjing · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2506.00289

Abstract

Joyce vertex algebras are vertex algebra structures defined on the homology of certain ℂ-linear moduli stacks, and are used to express wall-crossing formulae for Joyce's homological enumerative invariants. This paper studies the generalization of this construction to settings that come from non-linear enumerative problems. In the special case of orthosymplectic enumerative geometry, we obtain twisted modules for Joyce vertex algebras. We expect that our construction will be useful for formulating wall-crossing formulae for enumerative invariants for non-linear moduli stacks. We include several variants of our construction that apply to different flavours of enumerative invariants, including Joyce's homological invariants, DT4 invariants, and a version of K-theoretic enumerative invariants.

Citations

• Orthosymplectic Donaldson-Thomas theory
• Bordism categories and orientations of moduli spaces
• Intrinsic Donaldson-Thomas theory. II. Stability measures and invariants
• Intrinsic Donaldson-Thomas theory. I. Component lattices of stacks
• Cohomology of symmetric stacks
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• Equivariant K-theoretic enumerative invariants and wall-crossing formulae in abelian categories
• Enumerative invariants and wall-crossing formulae in abelian categories
• Counting sheaves on Calabi-Yau 4-folds, I
• The homology of moduli stacks of complexes
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• Representations of cohomological Hall algebras and Donaldson-Thomas theory with classical structure groups
• On the structure of instability in moduli theory
• Self-dual quiver moduli and orientifold Donaldson-Thomas invariants
• The Hall module of an exact category with duality
• Shifted Symplectic Structures
• Moduli of objects in dg-categories
• An Atiyah-Hirzebruch spectral sequence for KR-theory
• Paracategories I: internal parategories and saturated partial algebras
• Vertex Algebras and Algebraic Curves

Cited by

• Generalized intersection pairings on moduli spaces of vector bundles over a curve

Related

• Equivariant K-theoretic enumerative invariants and wall-crossing formulae in abelian categories
• Enumerative invariants in self-dual categories. II. Homological invariants
• A Course in Vertex Algebra
• Categorical Enumerative Invariants, I: String vertices
• Wall-crossing for Calabi-Yau fourfolds: framework, tools, and applications