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.
A description of the Goldman-Millson quasi-abelianity theorem within the framework of higher category theory is given in FM10.
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
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