Minimal models and Mori fibre spaces for generalized log canonical Q-pairs

Abstract — v1

We resolve the existence form of the minimal-model conjecture for projective generalized log canonical $\mathbb Q$-pairs over algebraically closed fields of characteristic zero. Such a pair admits a minimal model when its adjoint divisor is pseudo-effective, and a Mori fibre space otherwise, while keeping the nef $\mathbb Q$-Cartier b-divisor fixed. Taking the nef part to be zero gives the corresponding result for ordinary log canonical $\mathbb Q$-pairs.