Speaker: Chen Jiang (Fudan University)
Time: 10:00-11:00 a.m., June 6, Friday
Location: Room 1510, SIMIS
Abstract:
For varieties of general type, it is natural to study the distribution of birational invariants and relations between invariants. We are interested in the relation between two fundamental birational invariants: the geometric genus and the canonical volume. For a minimal projective surface $S$, M. Noether proved that $K_S^2\geq 2p_g(S)-4$, which is known as the Noether inequality. It is thus natural and important to study the higher dimensional analogue.
In this talk, I am going to present our recent progress in three dimensional Noether inequality. This is a joint work with Meng Chen and Yong Hu, based on earlier joint work with Jungkai Chen and Meng Chen. We will show that the inequality $\text{vol}(X)\geq \frac{4}{3}p_g(X)-{\frac{10}{3}}$ holds for all projective $3$-folds $X$ of general type, where $p_g(X)$ is the geometric genus and $\text{vol}(X)$ is the canonical volume.
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