Threefolds of general type fibered by surfaces with small volume

In birational classification theory, it is interesting to study the distribution and relations of birational invariants. Also, it is interesting to characterize those varieties with extremal invariants. In this talk, we are going to work on threefolds of general type fibered by surfaces with small volume. By combining the techniques of geometry of linear systems and minimal model theory, one can have quite explicit description of such kinds of threefolds. We will show applications to the study of Noether type inequality, Severi type inequality and threefolds with minimal volume.