chiral Dolbeault complex

The chiral de Rham complex sheaf of vertex operator algebras of a complex manifold admits a resolution by a fine sheaf which in degree-0 is the Dolbeault-resolution of the structure sheaf. This is the *chiral Dolbeault complex* (Cheung 10).

Where the construction of the chiral de Rham complex as a sheaf of vertex operator algebras requires the complex analog of a string structure in that the second Chern class vanishes, the construction of the chiral Dolbeault complex requires an analog of a differential string structure where a differential 3-form is chosen such that $\mathbf{d}H \propto \langle R \wedge R\rangle$.

- Pokman Cheung,
*The Witten genus and vertex algebras*(arXiv:0811.1418)

Created on March 21, 2014 at 09:08:48. See the history of this page for a list of all contributions to it.