Since the dgla $A^{0,*}(T_X)$ is a model for the derivedglobal sections $R\Gamma\mathcal{T}_X$ of the tangent sheaf $\mathcal{T}_X$ of $X$, the Goldman-Millson quasi-abelianity theorem can be stated by saying that if $X$ be a smooth complex manifold with trivial canonical bundle, then $R\Gamma\mathcal{T}_X$ 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$\mathbb{K}$, 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.

References

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

Revised on September 13, 2012 00:16:33
by Urs Schreiber
(82.169.65.155)