Shokurov's conjecture on conic bundles with canonical singularities. (9th June 2022) - Han, Jingjun; Jiang, Chen; Luo, Yujie
Abstract: A conic bundle is a contraction X→ Z between normal varieties of relative dimension 1 such that -K_X 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 12 -lc, and the multiplicities of the fibres over codimension 1 points are bounded from above by 2 . Both values 12 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.