Canonical Infinitesimal Deformations

Abstract

This paper gives a canonical construction, in terms of additive cohomological functors, of the universal formal deformation of a compact complex manifold without vector fields (more generally of a faithful $g$-module, where $g$ is a sheaf of Lie algebras without sections). The construction is based on a certain (multivariate) Jacobi complex $J(g)$ associatd to $g$: indeed $\mathbb{C}\oplus {\mathbb{H}}^0(J(g){)}^{\ast }$ is precisely the base ring of the universal deformation.

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