Abstract
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.
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Choi, S.R. On the dual of the mobile cone. Math. Z. 272, 87–100 (2012). https://doi.org/10.1007/s00209-011-0922-7
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DOI: https://doi.org/10.1007/s00209-011-0922-7
Keywords
- Log minimal model program
- Mobile cone
- Movable curve
- Non-ample locus
- Non-nef locus
- Cone theorem
- Contraction theorem