Modules and generalizations of Joyce vertex algebras
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917437950132224 |
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| author | Bu, Chenjing |
| author_facet | Bu, Chenjing |
| contents | Joyce vertex algebras are vertex algebra structures defined on the homology of certain $\mathbb{C}$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_00289 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modules and generalizations of Joyce vertex algebras Bu, Chenjing Algebraic Geometry Quantum Algebra Joyce vertex algebras are vertex algebra structures defined on the homology of certain $\mathbb{C}$-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. |
| title | Modules and generalizations of Joyce vertex algebras |
| topic | Algebraic Geometry Quantum Algebra |
| url | https://arxiv.org/abs/2506.00289 |