Shokurov’s conjecture on conic bundles with canonical singularities

A conic bundle is a contraction X→ Z between normal varieties of relative dimension $1$ such that -KX is relatively ample. We prove a conjecture of Shokurov that predicts that if X→ Z is a conic bundle such that X has canonical singularities and Z is Q -Gorenstein, then Z is always 1/2 -lc, and the multiplicities of the fibres over codimension $1$ points are bounded from above by $2$ . Both values 1/2 and $2$ are sharp. This is achieved by solving a more general conjecture of Shokurov on singularities of bases of lc-trivial fibrations of relative dimension $1$ with canonical singularities.