  In this paper, we establish a kind of Dolbeault type cohomology groups for
the purpose of studying the varying of complex structure invariants in
infinitesimal deformations of any order. We give a concrete description of the
higher order Kodaria-Spencer maps by using these cohomology groups. We
reformulate the obstruction formulas within the framework of these cohomology
groups and give a new proof for the formulas.

Algebraic Geometry