Noether-Severi inequality and equality for irregular threefolds of general type

Yong Hu, Tong Zhang

We prove the optimal Noether-Severi inequality that $\mathrm{vol}(X)\ge \frac{4}{3}\chi ({\omega }_X)$ for all smooth and irregular $3$-folds $X$ of general type over $\mathbb{C}$. For tho…