Conformal blocks on smoothings via mode transition algebras
Here we define a series of associative algebras attached to a vertex operator algebra $ V $,
called mode transition algebras, showing they reflect both algebraic properties of $ V $ and …
called mode transition algebras, showing they reflect both algebraic properties of $ V $ and …
On factorization and vector bundles of conformal blocks from vertex algebras
Representations of vertex operator algebras define sheaves of coinvariants and conformal
blocks on moduli of stable pointed curves. Assuming certain finiteness and semisimplicity …
blocks on moduli of stable pointed curves. Assuming certain finiteness and semisimplicity …
Conformal blocks from vertex algebras and their connections on ℳg, n
We show that coinvariants of modules over vertex operator algebras give rise to
quasicoherent sheaves on moduli of stable pointed curves. These generalize Verlinde …
quasicoherent sheaves on moduli of stable pointed curves. These generalize Verlinde …
On global generation of vector bundles on the moduli space of curves from representations of vertex operator algebras
C Damiolini, A Gibney - arXiv preprint arXiv:2107.06923, 2021 - arxiv.org
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 …
given by simple modules over certain vertex operator algebras, extending results for affine …
Convergence of sewing conformal blocks
B Gui - Communications in Contemporary Mathematics, 2024 - World Scientific
In a recent work [On factorization and vector bundles of conformal blocks from vertex
algebras, preprint (2019), arXiv: 1909.04683], Damiolini et al. showed that for a C 2-cofinite …
algebras, preprint (2019), arXiv: 1909.04683], Damiolini et al. showed that for a C 2-cofinite …
Factorization presentations
Modules over a vertex operator algebra V give rise to sheaves of coinvariants on moduli of
stable pointed curves. If V satisfies finiteness and semi-simplicity conditions, these sheaves …
stable pointed curves. If V satisfies finiteness and semi-simplicity conditions, these sheaves …
Conformal blocks in genus zero and the KZ connection
P Belkale, N Fakhruddin - Perspectives on Four Decades of Algebraic …, 2024 - Springer
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Unbounded field operators in categorical extensions of conformal nets
B Gui - arXiv preprint arXiv:2001.03095, 2020 - arxiv.org
We prove the equivalence of VOA tensor categories and conformal net tensor categories for
the following examples: all WZW models; all lattice VOAs; all unitary parafermion VOAs; type …
the following examples: all WZW models; all lattice VOAs; all unitary parafermion VOAs; type …
Lazy tournaments and multidegrees of a projective embedding of
We provide a new geometric interpretation of the multidegrees of the (iterated) Kapranov
embedding $\Phi_n:\overline {M} _ {0, n+ 3}\hookrightarrow\mathbb {P}^ 1\times\mathbb …
embedding $\Phi_n:\overline {M} _ {0, n+ 3}\hookrightarrow\mathbb {P}^ 1\times\mathbb …
Genus Zhu Recursion for Vertex Operator Algebras and Their Modules
MP Tuite, M Welby - arXiv preprint arXiv:2312.13717, 2023 - arxiv.org
We describe Zhu recursion for a vertex operator algebra (VOA) and its modules on a genus
$ g $ Riemann surface in the Schottky uniformisation. We show that $ n $-point (intertwiner) …
$ g $ Riemann surface in the Schottky uniformisation. We show that $ n $-point (intertwiner) …