Yong Hu, Noether Inequality for Irregular Threefolds of General Type

Let X be a smooth irregular 3-fold of general type. In this talk, we will prove that the optimal Noether inequality vol(X) ≥ (4/3) p_g(X) holds if p_g(X) ≥ 16 or if X has a Gorenstein minimal model. Moreover, when X attains the equality and p_g(X) ≥ 16, its canonical model will be explicitly described. This is a joint work with Tong Zhang.