We prove that the mobile cone and the cone of curves birationally movable in codimension 1 are dual to each other in the (K + B)-negative part for a klt pair (X, B). This duality of the cones gives a partial answer to the problem posed by Sam Payne. We also prove the cone theorem and the contraction theorem for the expanded cone of curves birationally movable in codimension 1.
All Science Journal Classification (ASJC) codes
- General Mathematics