Yong Hu, Moduli spaces of threefolds on the Noether line

In this talk, we will introduce the 3-dimensional Noether inequality and completely classify the canonical threefolds on the Noether line with $p_g \ge 5$ by studying their moduli spaces. For every such moduli space, we establish an explicit stratification, estimate the number of its irreducible components and prove the dimension formula. A new and unexpected phenomenon is that the number of irreducible components grows linearly with the geometric genus, while the moduli space of canonical surfaces on the Noether line with any prescribed geometric genus has at most two irreducible components of the same dimension. This is a joint work with S.Coughlan, R.Pignatelli and T.Zhang.