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A remark on the $C_2$-cofiniteness condition on vertex algebras

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arxiv 1004.1492 v2 pith:UJCVPWRV submitted 2010-04-09 math.QA

Tomoyuki Arakawa This is my paper · ORCID
classification math.QA
keywords cofinitenessconditionvertexalgebraalgebrasbeilinsoncofinitefeigin
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abstract

We show that a finitely strongly generated, non-negatively graded vertex algebra $V$ is $C_2$-cofinite if and only if it is lisse in the sense of Beilinson, Feigin and Mazur. This shows that the $C_2$-cofiniteness is indeed a natural finiteness condition.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Double Poisson (vertex) algebra cohomology

    math.RT 2025-09 accept novelty 8.0 of 10

    The authors define a completed double Poisson cohomology valid for all double Poisson brackets, and introduce three cohomology theories for double Poisson vertex algebras, with representation functor compatibility.

  2. Higgsless Lagrangian SCFTs and Strongly Finite VOAs

    hep-th 2026-07 conditional novelty 7.0 of 10

    Higgsless Lagrangian N=2 SCFTs are sparse (free vectors, one SO/USp quiver family, three sporadics); the VOAs of two sporadics are strongly finite and logarithmic.

  3. Vertex Superalgebras for Hypertoric Varieties and 3d Abelian Gauge Theories

    math.QA 2026-06 unverdicted novelty 7.0 of 10

    Constructs ħ-adic sheaves of vertex superalgebras on hypertoric varieties, proves the associated affine variety recovers the singular hypertoric one, establishes the 3d Higgs branch conjecture for abelian cases, and s...

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