Let be a smooth complex manifold with trivial canonical bundle, and let be the differential graded Lie algebra of smooth differential forms of type with coefficients in the tangent sheaf of . The Goldman-Millson quasi-abelianity theorem GM90 states that the dgla is quasi-abelian, i.e., it is quasi-isomorphic to an abelian dgla.
Since the dgla is a model for the derived global sections of the tangent sheaf of , the Goldman-Millson quasi-abelianity theorem can be stated by saying that if be a smooth complex manifold with trivial canonical bundle, then is quasi-abelian. In this form the Goldman-Millson theorem can be generalized to smooth projective manifolds over an arbitrary characteristic zero algebraically closed field , as done by Iacono and Manetti in IM10.
W. M. Goldman, J. J. Millson. The homotopy invariance of the Kuranishi space. Illinois J. Math. 34 (1990) 337-367.
D. Iacono, M. Manetti._An algebraic proof of Bogomolov-Tian-Todorov theorem_ Deformation Spaces. Vol. 39 (2010), p. 113-133; arXiv:0902.0732
D. Fiorenza, E. Martinengo. A short note on ∞-groupoids and the period map for projective manifolds Publications of the nLab. Vol. 2 (2012); arXiv:0911.3845