On the cohomology groups of a polarisation and diagonal quantisation

J. H. Rawnsley
1977 Transactions of the American Mathematical Society  
The sheaf SF(L) of germs of sections of a line bundle L on a manifold X covariant constant with respect to a flat connection defined for vectors in a complex subbundle F of the tangent bundle has a resolution by differential forms defined on F with values in L provided F satisfies the integrability conditions of the complex Frobenius theorem. This includes as special cases the de Rham and Dolbeault resolutions.
doi:10.1090/s0002-9947-1977-0648775-2 fatcat:t6iruflin5anzdgoe5inwldvje