A note on extended complex manifolds
S. A. Merkulov
Abstract
We introduce a category of extended complex manifolds, and prove that the functor describing deformations of a classical compact complex manifold M within this category is versally representable by (an analytic subspace in) H*(M,TM). By restricting the associated versal family of extended complex manifolds over H*(M,TM) to the subspace H1(M,TM) one gets a correct limit to the classical picture.
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