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arXiv · 1601.03314

Morphisms and faces of pseudo-effective cones

Mihai Fulger·Brian Lehmann
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Abstract

Let $π: X \to Y$ 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 one.

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Mihai Fulger, Brian Lehmann. 2016-01-13. Morphisms and faces of pseudo-effective cones. https://doi.org/10.1112/plms%2Fpdw008

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