Infinitesimal extension of pluricanonical forms

Abstract

The current paper represents the first part: it contains the results concerning the lifting of twisted canonical sections defined on an infinitesimal neighborhood of the central fiber of a smooth, proper Kähler family which verify a natural L2 condition.

Comments welcome. We have decided to split our work arXiv:2012.05063 into two parts (this is mainly due to its length)