Abstract:
A conic bundle is a contraction $X\to Z$ between normal varieties of relative dimension $1$ such that the anit-canonical divisor is relatively ample. In this talk, I will prove a conjecture of Shokurov which predicts that, if $X\to Z$ is a conic bundle such that $X$ has canonical singularities, then base variety $Z$ is always $\frac{1}{2}$-lc, and the multiplicities of the fibers over codimension $1$ points are bounded from above by $2$. Both values $\frac{1}{2}$ and $2$ are sharp. This is a joint work with Chen Jiang and Yujie Luo.
