2 Paul Bressler
نویسنده
چکیده
The purpose of this note is to give a “coordinate free” construction and prove the uniqueness of the vertex algebroid which gives rise to the chiral de Rham complex of [GMS]. In order to do that, we adapt the strategy of [BD] to the setting of vertex agebroids. To this end we show that the stack EVAX of exact vertex algebroids on X is a torsor under the stack in Picard groupoids ECAX of exact Courant algebroids on X (and, in particular, is locally non-empty). Moreover, we show that that ECAX is naturally equivalent to the stack of ΩX d −→ Ω X -torsors. These facts are proven for X a manifold (C , (complex) analytic, smooth algebraic variety over C). We leave to the reader the obvious extension to differential graded manifolds. Given a manifold X, let X denote the differential graded manifold with the underlying space X and the structure sheaf OX♯ the de Rham complex of X. We show that ECAX♯ is, in fact, trivial. Together with local existence of vertex OX♯-algebroids this implies that there exists a unique up to a unique isomorphism vertex algebroid over the de Rham complex. We give a “coordinate-free” description of the unique vertex OX♯-algebroid in terms of generators and relations.
منابع مشابه
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Author Affiliations: Universidade Nove de Julho, São Paulo, Brazil (Dr Lopes); and Retina Division, Wilmer Eye Institute, Johns Hopkins University School of Medicine and Hospital, Baltimore, Maryland (Drs ZayitSoudry, Moshiri, S. B. Bressler, and N. M. Bressler). Correspondence: Dr N. M. Bressler, Wilmer Eye Institute, Maumenee 752, Johns Hopkins Hospital, 600 N Wolfe St, Baltimore, MD 21287-92...
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