In 1990's, it was proved by Y.-T. Siu that plurigenera are invariant under smooth projective deformation. More generally, for deformation of Kähler manifolds, we can still expect similar invariance. However, such a general question is an open problem. Keeping this in mind, we study basics on the theory of deformation of complex structures.
In a series of lectures, we study the following for smooth deformation:
(1) We begin by discussing fundamental concepts such as the Kodaira-Spencer map and the Kuranishi family.
(2) It will be shown that Kählerity is preserved under small deformation.
(3) Related to variation of Hodge structure, Griffiths transversality will be discussed.
(4) Finally, we study the behavior of plurigenera under smooth deformation.