A note on extended complex manifolds

S. A. Merkulov

paper

A note on extended complex manifolds

arXiv:math/0005224

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) $H^{*} (M, T_{M})$ . By restricting the associated versal family of extended complex manifolds over $H^{*} (M, T_{M})$ to the subspace $H^{1} (M, T_{M})$ one gets a correct limit to the classical picture.

LaTeX, 12p