The Noether inequality for threefolds and three moduli spaces with minimal volumes

Meng Chen, Yong Hu, Chen Jiang

We establish the Noether inequality \[\textrm{Vol}(X)\geq \frac{4}{3}p_g(X)-\frac{10}{3}\] for all projective $3$-folds $X$ of general type with geometric genus $5\leq p_g(X)\leq 1…