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On the cohomology groups of a polarisation and diagonal quantisation
1977
Transactions of the American Mathematical Society
Preserved Fulltext
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