It seems a well-known fact that subvarieties of a variety of general type containing a general point are also of general type. This fact is essential properties used to prove some extension theorems of pluricanonical forms on algebraic variety of general type, see for example the very nice survey www-fourier.ujf-grenoble.fr/ECOLETE/2007/cours/pacienza.pdf. I want to know why this is true? Is there any thing more we can say about the relation between the canonical bundle of the variety and subvarities of codimension no less than 2.