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BIMSA 代数几何讨论班
BIMSA 代数几何讨论班
Subadditivity of anticanonical Iitaka dimension in characteristic p>0
Subadditivity of anticanonical Iitaka dimension in characteristic p>0
演讲者
Iacopo Brivio
时间
2026年06月11日 10:00 至 11:00
地点
A7-201
线上
Zoom 638 227 8222
(BIMSA)
摘要
The Iitaka conjecture predicts that if $f:X \to Y$ is a fibration of smooth complex projective varieties and $y\in Y$ is a general point, then $\kappa(K_X)\geq \kappa(K_{X_y})+\kappa(K_Y)$. It was shown by Chang that, if the stable base locus $B(-K_X)$ does not dominate $Y$, then $\kappa(-K_X)\leq \kappa(-K_{X_y})+\kappa(-K_Y)$. Both the Iitaka conjecture and Chang's theorem are false in characteristic $p>0$. However the expectation is that one should be able to recover these inequalities when a general fiber is sufficiently "well behaved" with respect to the action of Frobenius. In this talk I will discuss how to recover Chang's theorem for such a class of fibrations, and discuss some related questions. This is based on a joint work with M. Benozzo and C.K. Chang.