Morphisms and faces of pseudo‐effective cones

@article{Fulger2016MorphismsAF,
  title={Morphisms and faces of pseudo‐effective cones},
  author={Mihai Fulger and Brian Lehmann},
  journal={Proceedings of the London Mathematical Society},
  year={2016},
  volume={112}
}
Let π:X→Y be a morphism of projective varieties and suppose that α is a pseudo‐effective numerical cycle class satisfying π*α=0 . A conjecture of Debarre, Jiang, and Voisin predicts that α is a limit of classes of effective cycles contracted by π . We establish new cases of the conjecture for higher codimension cycles. In particular, we prove a strong version when X is a fourfold and π has relative dimension 1. 

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