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Seminar
FIELD Math:Geometry
DATE October 28 (Thu), 2021
TIME 16:00-17:00
PLACE Online
SPEAKER Hu, Yong
HOST Meng, Sheng
INSTITUTE Shanghai Jaio Tong University
TITLE Noether-Severi inequality and equality for irregular threefolds of general type
ABSTRACT We prove the optimal Noether-Severi inequality that $\vol(X) \ge \frac{4}{3} \chi(\omega_{X})$ for all smooth and irregular $3$-folds $X$ of general type over $\CC$. This answers an open question of Z. Jiang in dimension three. For those $3$-folds $X$ attaining the equality, we completely describe their canonical models and show that the topological fundamental group $\pi_1(X) \simeq \ZZ^2$. As a corollary, we obtain for the same $X$ another optimal inequality that $\vol(X) \ge \frac{4}{3}h^0_a(X, K_X)$ where $h^0_a(X, K_X)$ stands for the continuous rank of $K_X$, and we show that $X$ attains this equality if and only if $\vol(X) = \frac{4}{3}\chi(\omega_{X})$. This is a joint work with Tong Zhang.

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